















- 




RARY, 




SI 



3S 



■ses. and 



7-7^ ;— ' Hts each. 

GEOMETRY. By H. 



PRACTICAL PLANE AND SOLID 

Angel, Islington Science School, London. 
2. MACHINE CONSTRUCTION AND DRAWING. 

Tomkins, Queen's College, Liverpool. 
3ABUIL 




Wc 
3BBUIL 
R. 

4. NAVi 
By 

5. PURI 
L01 

6. THE( 
F.C 

7. APPL \ 
Lot 

8. ACOl 
Lee 

9. MAGI 
Scic 

10. INOR 
Dul 

11. ORG^ 
Gra 

12. GEOL 

13. MINE 
tech 

14. ANIM 

Mas 

15. ZOOL 

Ne\ 

16. VEGE 

Ball 

17. SYSTLiVirV 1 XV> XXl-H XJ ii,V_,Vyi>IV_7J.VlJ.\_x JL)V 1 ni> I 

M.D., Edinburgh University. 

19. METALLURGY. By John Mayer, F.C.S., Glasgow. 

20. NAVIGATION. By Henry Evers, LL.D., Plymouth. 

21. NAUTICAL ASTRONOMY. By Henry Evers, LL.D. 

22A STEAM AND THE STEAM ENGINE— Land and Marine. 

By Henry Evers, LL.D., Plymouth. 
22B STEAM AND STEAM ENGINE— Locomotive. By Henry 

Evers, LL.D., Plymouth. 

23. PHYSICAL GEOGRAPHY. By John Macturk, F.R.G.S. 

24. PRACTICAL CHEMISTRY. By John Howard, London. 

25. ASTRONOMY. By J. J. Plummer, Observatory, Durham. 



Class 
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By E. 
and Slate 
n Work. By 
Laying off. 
3. A., (Camb.,) 
;iter, F.R.A.S., 
er, F.R.A.S., 
a Lees, A.M., 
Angell, Senior 
ead, F.R.A.S., 
D.Sc, (Lond.,) 

'ornwall Poly- 
mior Science 
)del Schools, 
[. By J. H. 
xjy J. H. Balfour, 



IN COTJRS 



;E OP PTOMq^TION. 
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IES. 



Adapted to the requirements of Students in Science and Art Classes, and 
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Printed uniformly in i2mo, averaging 350 //., fully Illustrated, cloth 

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1. PRACTICAL PLANE AND SOLID GEOMETRY. By Professor 

F. A. Bradley, London. 

2. MACHINE CONSTRUCTION AND DRAWING. By E. 

Tomkins, Queen's College, Liverpool. 

3. BUILDING CONSTRUCTION. By R. Scott Burn, C.E. 

4. NAVAL ARCHITECTURE— Shipbuilding and Laying off. 

By S. J. P. Thearle, F.R.S.N.A.. London. 

5. PURE MATHEMATICS. By Edward Atkins, B.Sc, (Lond.,) 

Leicester. 2 vols. 

6. THEORETICAL MECHANICS. By P. Guthrie Tait, Professor 

of Natural Philosophy, Edinburgh. 

7. APPLIED MECHANICS. By Professor O. Reynolds, Owens 

College, Manchester. 

8. ACOUSTICS, LIGHT AND HEAT. By W. S. Davis, LL.D., 

Derby. 

9. MAGNETISM AND ELECTRICITY. By F. Guthrie, B.A., 

Ph.D., Royal School of Mines, London. 

10. INORGANIC CHEMISTRY. By T. E.Thorpe, Ph.D., F.R.S.E., 

Professor of Chemistry, Andersonian University, Glasgow. 
2 Vols. 

11. ORGANIC CHEMISTRY. By James Dewar, F.R.S.E., F.C.S., 

Lecturer on Chemistry, Edinburgh. 

12. GEOLOGY. By John Young, M.D., Professor of Natural History, 

Glasgow University. 

14. ANIMAL PHYSIOLOGY. By J. Cleland, M.D., F.R.S., Professor 

of Anatomy and Physiology, Galway. 

15. ZOOLOGY. By E. Rav Lankester, M.A., (Oxon.,) London. 

16. VEGETABLE ANATOMY AND PHYSIOLOGY. By J. H. 

Balfour, M.D., Edinburgh University. 

17. SYSTEMATIC AND ECONOMIC BOTANY. By J. H. Balfour, 

M.D., Edinburgh University. 

19. METALLURGY. By W. H. Greenwood, A.R.S.M. 2 Vols. 

20. NAVIGATION. By Henry Evers, LL.D., Professor of Applied 

Mechanics, Plymouth. 

21. NAUTICAL ASTRONOMY. By Henry Evers, LL.D., Plymouth. 

22. STEAM AND THE STEAM ENGINE— Land, Marine, and 

Locomotive. By Henry Evers, LL.D., Plvmouth. 

23. PHYSICAL GEOGRAPHY. By John Young, M.D., Professor of 

Natural History, Glasgow University. 






i& 




Total Eclipse op the Sun, Aug. 7th 1869 
Showing the Corona and Prominences. 



^utitjrm'iS '<$Uttttnt»rg $titntt $tnt$ 



INTRODUCTION 



TO 



ASTRONOMY 



FOR THE USE OF SCIENCE CLASSES AKD 

ELEMENTARY AND MIDDLE CLASS 

SCHOOLS. 



BY 
JOHN ISAAC PLUMMER, 

ASTRONOMICAL OBSEEVEB TO THE UNIVERSITY OF DUBBA.M. 




NEW YORK: 

G. P. PUTNAM'S SONS, 

FOURTH AVENUE AND TWENTY-THIRD STREET. 

1873. 






By Transfer from 
U.S. Naval Academy 
Aug. 26 1932 



PEEFACE 



The present Work is intended to supply a want which 
has been felt for a long time by those engaged in the 
scientific education of the young. Astronomy has not 
been generally cultivated in this country to nearly the 
extent that it has been, and still is, upon the Continent 
and in America; and it is believed that this is in some 
part owing to the want of elementary works on the sub- 
ject. They must be sufficiently cheap to form class-books 
for middle-class schools, sufficiently scientific to imbue the 
youthful mind with a love for the science in its true aspect, 
and yet at the same time sufficiently easy and free from 
technicalities and mathematical reasoning to be read and 
understood with the imperfect knowledge of pure mathe- 
matics, possessed by this class of students. Such then has 
been the aim of this Work. 

It has also been particularly prepared to meet the wants 
of students in Physical Geography, of whom some know- 
ledge of Astronomy is very properly required by the Ex- 
aminers of the Science and Art Department at South 
Kensington. It will therefore be found that all those 
branches which have an especial bearing upon the subject 
of terrestrial physics have been treated at greater length. 
The whole, however, forms an introduction to the study 
of Astronomy, which it is hoped may lead some to seek 
for deeper knowledge in other more advanced works, and 
in the standard text-books of the Universities. 

As a means of enlarging the mind and of elevating the 
understanding, no one of the applied sciences can compare 
with Astronomy; and it is to be regretted that so much 
profound ignorance of its truths prevails among even well 



IV PREFACE. 

educated persons. Yet it is beginning to be admitted, 
that no education can be considered perfect that does not 
include a knowledge of the simple facts of Astronomy, and 
along with other branches of science, it is now being 
gradually introduced into our schools. 

All the dimensions of the Solar System, <fcc., that 
depend upon the value of the Solar Parallax, have been 
recomputed with the assumed value 8" -94, in favour of 
which the Author believes the mass of evidence at present 
to incline. A similar correction has been made in other 
recent works, but the new values to which it gives rise 
in several instances, have not been calculated with the 
precision, nor followed throughout all the terms which 
are affected by the alteration as carefully as desirable. 
Although the Solar Parallax is assumed provisionally, 
there is no reason why it should not be treated as an 
accurate value till one still more reliable is discovered. 
Occasionally these emendations having been made by un- 
professional astronomers have given rise to strange mis- 
takes. Though the Author cannot hope that the present 
work is entirely free from error, yet the calculations have 
been carefully made, and it is believed they will be found 
generally correct. 

A more advanced text-book still seems to be a 
desideratum. 

J. I. P 



The Observatory, Durham, 
December, 1872. 



CONTENTS. 



CHAPTER I. 



PAGE 
9 



I. FORM AND DIMENSIONS OF THE EARTH, . 

II. ROTATION OF THE EARTH ON ITS AXIS, . . 13 

III. THE ATMOSPHERE — REFRACTION AND TWILIGHT, 19 



QUESTIONS, 



24 



CHAPTER II. 

I. OF THE VARIOUS MODES OF DEFINING THE 

POSITIONS OF CELESTIAL OBJECTS, 
II. OF THE INSTRUMENTS NECESSARY TO DETERMINE 
THE POSITION OF A HEAVENLY BODY, . 

III. EXTRA MERIDIONAL INSTRUMENTS, . 

IV. MEASUREMENT OF TIME — THE CALENDAR, . 
QUESTIONS, 



27 

32 
38 
40 
44 



CHAPTER III. 

I. LAWS OF PLANETARY MOTION, . 
II. OF THE UNIVERSAL LAW OF GRAVITATION, 

III. PARALLAX, . . . . 

IV. THE ABERRATION OF LIGHT, . 
QUESTIONS, 



46 
51 
56 
62 
64 



VI 



CONTENTS. 



CHAPTER IV. 

I. THE SOLAR SYSTEM, . 
II. THE SUN, : 

INFERIOR PLANETS 

III. MERCURY, . 

IV. VENUS, 

QUESTIONS, . 



PAGE 

66 

70 



80 
83 
So 



CHAPTER V. 



I. THE EARTH, 
II. DENSITY OF THE EARTH, 
III. THE MOON, 



IV. ECLIPSES,. 



QUESTIONS, 



88 

93 

97 

105 

112 



CHAPTER VI 

SUPERIOR PLANETS 

I. MARS, 
II. THE ASTEROIDS 

III. JUPITER, . 

IV. SATURN, . 
V. URANUS, . 

VI. NEPTUNE,. 
QUESTIONS, 



115 

118 
120 
126 
130 
132 
134 



CONTENTS. Vll 

PAGE 

CHAPTER VII. 

I. COMETS, 137 

QUESTIONS, ....... 147 

CHAPTER VIII. 

PERTURBATIONS, 149 

I. THE TIDES, ....... 149 

II. PRECESSION OF THE EQUINOXES — NUTATION, . 151 

III. LUNAR AND PLANETARY PERTURBATIONS, . 154 

QUESTIONS, ....... 156 

CHAPTER IX. 

SIDEREAL ASTRONOMY 

I. OF THE FIXED STARS, 158 

II. OF DOUBLE AND VARIABLE STARS, . . .162 

III. CLUSTERS OF STARS NEBULA, . . .167 

QUESTIONS, 169 



ASTBONOMY. 



CHAPTER I. 



I. FORM AND DIMENSIONS OF THE EARTH. 

Before we can learn anything of the motions, distances, 
or magnitudes of the heavenly bodies, it is necessary that 
we should have correct ideas of the size and form of the 
Earth itself. That its surface is curved, and its whole 
figure more or less spherical, appears from the following 
considerations : — (1.) When a ship is leaving port, the 
mariner sees the erections upon the shore gradually sink 
below the sea-offing or horizon, the foundations and lower 
stories disappearing first, until the whole is hid. Should 
he now climb to the mast-head, he will see the whole re- 
appear in the opposite order. The simple effect of dis- 
tance, however, is to diminish the size and the brightness 
of objects, in no way altering their forms. It is, there- 
fore, only to be explained by the fact, that the surface of 
the ocean is curved, and rises up between the ship and the 
shore. .From the height of the mast it is possible to look 




Fk 1. 



over this curvature ; yet, as the distance becomes still 
greater, the buildings on the coast will sink below the 
visible horizon, notwithstanding the altitude of the spec- 
tator. While the view of an observer at the sea-level is 



10 ASTRONOMY, 

limited by a plane passing through the eye parallel to 
the surface of smooth water, one situated at a height, as 
on the deck or mast of. a ship, is able to see somewhat 
below this. The depression of the sea-offing is known as 
the Dip of the Horizon, and forms a constant correction 
for all observations made at sea. Thus, if ANP repre- 
sent a portion of the earth, the view of an observer at £T 
is bounded by the line IT N ; while an observer on a 
mountain at Z would see all the first observer could, and 
in addition that portion of the heavens between O and S, 
— the arc S O', measured on the celestial sphere, being the 
dip of the horizon at the altitude Z N. 

(2.) A similar proof of the earth's roundness is found 
in a phenomenon that has been sometimes observed by 
aeronauts, when ascending very soon after sunset. As 
they rise rapidly in the air, the sun comes again into 
view, rising gradually on their western horizon, while the 
earth below them is in profound shadow. If the earth 
were a flat plane, it is clear that even a slight depression 
of the sun below the horizon would cast in shadow the 
highest altitudes which the aeronaut could reach. 

(3.) If the level of a surveyor be employed upon the 
surface of the still water of a canal, it will be found that 
at the distance of one mile the water is depressed below 
the level of the instrument about eight inches. This 
affords not only a proof of the earth's form, but some idea 
of its size. A globe will require to have a diameter of 
about 7,920 miles to have a curvature equal to that 
observed on the canal, and this may be taken as a very 
fair approximation to the diameter of the earth. 

(4.) Beyond this there is the evidence of lunar eclipses, 
which phenomena are palpably caused by the shadow of 
the earth falling upon the full moon. The outline of the 
shadow is alivays circular, and no other figure than a 
sphere will cast a circular shadow in whatever direction 
the light may fall upon it. 

(5.) There is the noi unimportant fact of the circum- 
navigation of the globe in every direction which the 
configuration of the land will allow. 



FORM AND DIMENSIONS OF THE EARTH. 11 

To obtain more accurate information of the earth's form 
and dimensions, it is necessary to determine the distance 
between two remote points on its surface which are upon 
the same meridian, or due north and south of each other, 
with the greatest possible care, and then by celestial ob- 
servation to learn what fractional part of the earth's 
circumference has actually been measured — an operation 
of the greatest difficulty in practice, but achieved in the 
following manner. A portion of country is selected where 
the ground is very nearly level, and a base line is marked 
out. Bars of metal are prepared as measuring rods with 
every care, and these are placed end to end along the 
base line, accurately levelled. They are not allowed to 
touch, lest some accident or expansion of the bars should 
cause them to jolt one against another, but the intervals 
are measured by microscopes, and the temperature of the 
bars observed, in order that their expansion from heat 
may be calculable j they are also protected from the rays 
of the sun by tents, when being used. This process is 
repeated, again and again, along the line with the same 
rods, till a distance of a few miles is measured with great 
accuracy, the two extremities being rigorously marked. 
A third station is now taken into account, generally 
selected upon the summit of a conspicuous hill, and its 
bearing is found by means of theodolites stationed 
at either extremity of the base line. It will be seen that 
this line and the lines joining each extremity of it to the 
third station will form a triangle, of which the length of 
one side is known, and also the amplitude of two of the 
angles. It becomes then a very simple problem in trigo- 
nometry to calculate the lengths of the remaining sides.* 
Other stations are now chosen, and the newly-found dis- 
tances of the third station are in their turn taken as the 

* Those unacquainted with the principles of the mathematical 
solution of triangles will obtain some aid in understanding the 
above, by drawing triangles with the aid of compasses, &c. , of 
which the base and two angles are given quantities. It will at 
once be seen that these data determine the magnitude of the 
triangles, and that the trigonometrical solution is nothing more 
than a reduction to calculation of a simple geometrical problem. 



12 ASTRONOMY. 

bases of other larger triangles to be treated in the same 
manner. A net-work of triangles is thus formed, spread- 
ing over the country in a northern and southern direction, 
till the exact distance between two remote stations upon 
the same meridian of longitude is ascertained. In Bri- 
tain, trigonometrical surveys in this manner have been 
several times performed, the object being the distance in 
feet between a point on Shanklin Down, Isle of Wight, 
and one on the island of Balta, in Shetland. This is 
called the great meridional arc of England; and several 
base lines have been measured at different times for its 
verification — notably at • Loch Foyle in Ireland — for it 
should be remarked that very large triangles are often 
chosen, and a considerable arm of the sea is passed over 
without difficulty. We have now to find what fractional 
part of the earth's circumference has been measured. The 
direction of the plumb-line is not parallel to itself at 
different places, but is always towards the earth's centre. 
It may therefore be considered as a prolongation of the 
earth's radius at any point. Suppose that at one ex- 
tremity of the meridional arc, it points to a particular 
star,' and at the other extremity it is found to point 10° 
to the south of that star, then the angle contained 
between the radii of the earth at these points is 10°, or 
3^-part of the earth's circumference. An instrument, 
called a zenith sector, is used to ascertain the direction of 
the plumb-line, in space or with reference to the stars, at 
the two stations. In this manner the length of 1° of 
latitude is found to be about 69*1 miles \ and hence the 
whole circumference w T ill equal 24,876 miles, and the 
diameter 7,918 miles, roughly. 

The importance of the problem has led to similar 
measurements being made in various parts of the world. 
The most celebrated arcs are those of Russia, France, 
England, India, Peru, and the Cape of Good Hope — places 
differing greatly in latitude — which brings to light this 
important fact. The length of a degree of latitude in 
feet always decreases slightly as the equator is reached, 
showing that the curvature there is greatest, or, in other 



ROTATION OF THE EARTH ON ITS AXIS. 13 

words, that the earth is not a perfect sphere, but slightly 
flattened at the poles. Its figure is therefore that of 
an oblate spheroid. The numerous results have been 
thoroughly investigated by the accomplished mathema- 
ticians, Airy and Bessel. They agree in giving the 
following as the true dimensions of the earth : — 

Polar diameter, 7899.1 miles. 

Equatorial diameter, .... 7925*6 „ 
Difference or polar compression, . . 26*5 ,, 

Proportion of diameters, . . . 298 to 299 

These results are further confirmed by similar trigono- 
metrical surveys, carried in an east and west direction, 
the difference of longitude of the extreme stations being 
determined by methods to be afterwards explained. It is 
only necessary to state that similar dimensions and a like 
compression is found by these operations. 

II. ROTATION OF THE EARTH ON ITS AXIS. 

The first fact that attracts the attention of a person 
endeavouring to learn something of the heavens from 
actual inspection, rather than from books, is the diurnal 
motion of the stars. A few hours' observation of the 
heavens upon a starry night suffices to show a motion of 
all the stars from east to west. If any person will 
station himself so as to have a full view of the northern 
portion of the sky, he will soon find one star there that 
appears to be fixed. This is the pole star, which, revolves 
in so small a circle that its motion is not easily detected 
by the unaided eye. He will see further that stars very 
near the pole star revolve slowly in small circles round it, 
or, more strictly, a point near it, as a centre, and that as 
he selects stars for observation further removed from the 
pole, their motion is faster, but always circular round the 
same point, and performed in the same time (24 hours). 
At length he will find the circles become so large that the 
stars are seen to set below the horizon and rise again, after 
an interval, in order to complete their paths, If he now 



14 ASTRONOMY. 

stations himself to watch the southern heavens, he will see 
the stars rising obliquely from the eastern horizon, 
climbing to a considerable height in the south, and then 
declining and setting in the west. They will describe 
large arcs of circles, and move more rapidly than in the 
north. Stars in the extreme south will be seen only a 
short time, by far the larger part of their circular paths 
being performed below the horizon. If aided by a tele- 
scope, he will also notice that the low southern stars 
move with less velocity, showing a return to the condition 
of the northern heavens. Everywhere the same relative 
positions of the stars among themselves is preserved, and 
they appear to revolve as if attached to the interior of a 
hollow sphere, the axis of that rotation lying between the 
north pole, which is high above the northern horizon in 
these latitudes, and the south pole, which is equally 
depressed below the southern. Erom this general move- 
ment of the stars, one of two conclusions must be 
drawn — either the heavens revolve as a whole around the 
earth in a day, from east to west, or the earth revolves on 
its own axis, in the opposite direction, west to east. 
From the consideration of the very great distances of the 
heavenly bodies, of which rude notions might be obtained 
from certain phenomena which occasionally take place, 
as eclipses, occultations of the fixed stars by the moon, 
&c., the first of these hypotheses might be shown to be 
extremely improbable, if not absurd; but some simple 
experiments are possible, which more certainly point out 
this rotatory motion of the stars to be produced by the 
revolution of the earth on its axis. 

The first is known as Foucault's pendulum experiment. 
If a heavy ball of lead be suspended by a long wire from 
a fixed support, and be made to oscillate in the plane of 
the meridian above a table upon which the north and 
south points are marked, it will be noticed, after a short 
interval, to deviate from the direction of the meridian 
very sensibly, the oscillations on the southern side of the 
table turning towards the west. (The experiment is 
supposed to be made in the northern, hemisphere.) Now, 



ROTATION OF THE EARTH ON ITS AXIS. 15 

oy the principles of dynamics, the plane of oscillation of 
such a pendulum is invariable; and the cause of the devia- 
tion must be traced to the fact that the table has revolved 
to some extent, being carried round with the earth. 
Could this experiment be tried at either of the poles of 
the earth, the pendulum would follow the course of the 
stars exactly, as there the table would be at right angles 
to the axis of the earth's rotation, or would revolve on its 
own centre; on the contrary, at the equator the experi- 
ment would fail completely. 

An instrument called a gyroscope was also devised by 
M. Foucault, which still more plainly demonstrates that 
the motion of the stars is only apparent, that of the earth 
real; but the construction of this instrument, and the 
conditions to be fulfilled in using it, are too complicated 
to be described here. 

We have now to discuss an experiment which is at once 
a proof of the earth's rotation and of its deviation from a 
strictly spherical form. All are familiar with the influence 
of centrifugal force when a weight is made to revolve at 
the end of a cord. It tends to make the weight fly off 
from the centre of rotation. If the earth is really 
revolving, objects at the equator will be more subject to 
this force than in high latitudes. In other words, the 
weight of a body or the force of gravity will be less at the 
equator than at the poles. From the dimensions of the 
earth and the time of its rotation, it may be determined 
that the weight of a body will be reduced by -^g- in conse- 
quence of the centrifugal force acting at the equator. 
There are two methods by which the difference of gravity 
at two places may be ascertained experimentally: — 1st, 
The length to which a metallic spiral spring is stretched 
may be noted at the two places— in which case a weight of 
288 oz. near the poles would stretch it as much as 289 oz. 
at the equator, supposing the centrifugal force alone be 
taken into account. 2d, The vibrations of a pendulum at 
the two places in a given time may be counted. Since the 
velocity of the pendulum vibrations is directly dependent 
upon the force of gravity, this forms an admirable method 



16 ASTRONOMY. 

of determining its variation. Thus, when a pendulum 
that keeps true time at Melville Island (K lat. 74°22') is 
carried to the equator, it loses about 213 seconds in a day, 
its vibrations are slower to that extent, and hence gravity 
at the equator is less than at the poles.* Repeated 
observations of this kind have given y-^- as the difference 
in the force of gravity at the equator and poles; but we 
have seen that only -^-g- is to be attributed to the effect of 
centrifugal force arising from the rotation of the earth. 
The difference, or -^77, is therefore to be ascribed to the 
greater distance of the surface of the earth from the 
centre at the equator, than at the poles.t 

The reader will perceive, from what has been said of 
centrifugal force, that had the earth been a perfect sphere 
in rotation, it could not long have retained that form; the 
fluid portion at least would speedily have sought the 
equatorial regions, forming a protuberance there, and 
leaving two large polar continents. Newton has calcu- 
lated the ellipticity or amount of flattening of the earth, 
supposing it to have consisted at one time of fluid matter 
of uniform density revolving at the speed with which it 
now moves. He found the proportions of the diameters 
would be as 229 to 230 — which is not far removed from 
what its real ellipticity is. This is not put forward a* an 
explanation of the cause of the earth's flattened form, but 
as exhibiting the accordance of theory with fact, and in 
proof that the oblate spheroid is the figure of equilibrium, 
by virtue of which the waters of the ocean have no deter- 

* It is to he remarked that, in order to keep true time, the 
length of a pendulum beating seconds must vary in different lati- 
tudes, being shortest at the equator. Thus, at Melville Island the 
pendulum at the sea level must be 39*203 English inches, i^t 
Greenwich (N. lat. 51°. 29') 39*139 inches, and at the equator 
39-020 inches. 

1* This statement may be made in the following form: — A weight 
of 194 pounds, carried from the vicinity of the poles to the equator, 
would be found to weigh 193 pounds — ^±<§ of its weight, or 10 J oz., 
being lost in consequence of the centrifugal force acting there, and 
.]_, or d\ oz., in consequence of its greater distance from the centre 

of the earth, 



TRADE-WINDS. 17 

niination to any particular portion of its surface. We 
shall see later, when we come to speak of other planets 
than the earth, that all of them revolve on their own 
axes, and, like it, are flattened more or less at their poles ; 
so that analogy alone would lead us to conclude the same 
to be the case with the earth, had not more than sufficient 
proof already been adduced of the fact. 

Amongst other phenomena which depend upon the 
earth's diurnal motion around its own axis, that of the 
Trade-Winds stands pre-eminently first in importance. 
On either side of the equator the wind, especially on the 
ocean, blows almost constantly in one direction, being 
N.E. in the northern hemisphere and S.E. in the 
southern. The sun, as we shall soon learn, is at all times 
of the year vertical over some point or other within a 
limited space on either side of the equator, known as the 
tropics; and in consequence of this, that portion of the 
globe and the incumbent atmosphere is considerably 
warmer than at other parts. This heated atmosphere, 
following the general law of heat, expands greatly, and 
becomes specifically lighter than before, which causes it to 
rise to a high altitude, and its place is occupied by colder 
and heavier air from more temperate climates. The hot 
air slowly floats away above the cold air, which has taken 
its place next the surface. Gradually it is cooled down 
in higher latitudes, and it then descends and takes the 
place of the air removed to the equatorial regions; and in 
this manner a constant circulation is kept up. A wind 
near the surface, blowing perpetually from the direction 
of the poles to the equator, and an upper current of 
heated air, flowing from the equator towards the poles, 
would be the inevitable result if the earth was stationary 
and the sun revolved around it in the course of a day; 
but the rotation of the earth on its axis from west to east 
materially modifies this. The atmosphere, everywhere 
taking part in this rotation, travels with the earth at a 
similar speed ; but at the equator the distance from the 
axis of revolution being the greatest, the speed is likewise 
the greatest. Thus, the equatorial circumference of the 



18 ASTRONOMY. 

earth being 24,899 miles, the velocity of the atmosphere, 
when it appears stationary above the surface, must be 
equal to 1,040 miles per hour. At the latitude of 40° 
the circumference of the circle of latitude is only 19,060 
miles, and the velocity there will scarcely equal 800 miles 
per hour. The polar wind, in its course to the equator, 
does not acquire the increased velocity immediately upon 
entering the tropics, but lags behind the earth in these 
parts; and thus an easterly tendency is produced, giving 
rise, as before stated, to a north-east trade-wind in this 
hemisphere, and a south-east trade- wind in the southern. As 
it proceeds onward, however, the velocity is increased from 
constant friction against the surface, and it thereby partially 
loses its easterly character. Now, near the equator, the 
circles of latitude increase in dimensions very slowly, the 
diurnal motion of these portions of the earth likewise 
increases but slowly, and hence the trade-wind still 
further approaches to the direction of a polar current. 
Finally it meets the trade-wind setting in from the other 
hemisphere, and loses all the appearance of a permanent 
wind at the equator, which is usually a region of calms. 

It has further been remarked of late years that the 
direction of rotation of the cyclones and hurricanes which 
infest sub-tropical seas, is determined by the diurnal 
motion of the earth. These fearful tempests are produced 
by the unusual heating of some portion of land or water 
from local causes. The incumbent air being also greatly 
heated, rises, leaving a much reduced barometric pressure. 
Winds then set in from all parts to fill up the vacancy : 
that arriving from a polar direction, as in the case of the 
trade-winds, lagging behind somewhat, not having suffi- 
cient velocity; that from the equator, on the contrary, 
will have too great a velocity ; while winds from the east 
or west have no effect upon the gyratory motion of the 
cyclone. If we confine ourselves to the northern hemi- 
sphere for the present, it is clear that the polar or north 
wind will become a north-east wind, and that the equa- 
torial or south wind will become a south-west wind. 
Now, plainly, a wind blowing from the north-east will 



THE ATMOSPHERE. 19 

have the tendency, upon entering the vortex, to carry it 
round in the direction N", W, S, E, N. The equatorial 
current will also have the same effect. This is then the 
direction of revolution for cyclones in this hemisphere, 
while in the southern the reverse direction, or N, E, S,W, N" 
is taken. The latter conforms to the movement of the 
hands of a watch; the former is opposed to that move- 
ment. The explanation here given has been observed to 
aa'ree with fact ; and hence we have one more indication 
of the earth's daily revolution on its axis. 

III. THE ATMOSPHERE. 

There is one consideration more which it is necessary 
to examine before we attempt any observations upon 
celestial phenomena. The earth we all know to be 
enveloped by a thin film of very light gas, or more cor- 
rectly, mixture of gases, called air. Through this every 
observation of the heavens must be made, and its influence 
in modifying phenomena must be understood, before we 
can be satisfied of the accuracy of scientific inquiry. 
Though light, the air has weight : a globe of glass, from 
which the air has been exhausted, weighs less than it 
does when the air is re-admitted. Like other gases, also, 
it is compressible ; that is to say, two or more volumes of 
air may be forced into the same globe ; and, finally, it is 
elastic, or will diffuse itself, if subject to no compression, 
in a space greater than it ordinarily occupies. The con- 
stitution of the atmosphere will therefore be, that at the 
sea-level, the air having to bear the whole weight of that 
above it, will be compressed, dense, and heavy. As we 
ascend, it will get lighter and lighter, and finally will be- 
come so rarified that no absolute limit can be fixed as its 
termination. The rate of diminution of the density, as 
determined by its pressure upon the surface of mercury in 
the barometer, is very rapid ; so that at a height not 
exceeding that of many of our mountains (18,000 feet), one- 
half of the atmosphere would lie below and one half above 
the observer. At this height, the air being only half the 




20 ASTRONOMY. 

density at the sea-level, respiration is difficult, and at 
still higher altitudes no living creature could live. At 
forty or fifty miles above the surface of the earth the air 
would be so rarified that it would be impossible to deter- 
mine its existence by any means at our command; and 
this altitude may practically be taken as the limit to 
which the atmosphere extends. 

When a ray of light enters a fluid more or less dense 
than that from which it comes, obliquely, it is bent out of 
its course, agreeably to a well known law in optics. A 

very simple experi- 
ment will illustrate 
this, and is worth de- 
scribing, from its close 
analogy with what 
takes place when the 
light from a star enters 
the atmosphere. Let 
H K P Q be a vessel, 
g * having a point on the 

bottom, P, clearly marked. The observer's eye must be 
placed at A, so that P shall just be discernible over the 
margin. If the vessel be filled with water, the point will 
be seen upon the bottom at K. The line of sight from A, 
after touching the surface of the water at S, is bent out of 
its course in such a manner as to be more perpendicular 
to the surface than before reaching it, and thus arrives at 
the point P. But the observer is only sensible of the 
direction in which the light comes to his eye, namely, 
S A, and the point therefore is seen to be in that direc- 
tion, or at R. This effect upon light is called refraction. 
We will now consider what is the effect of refraction 
upon the light of a star. The atmosphere is a fluid denser 
than that through which the light of the star comes to 
us. It may be regarded as consisting of a series of layers, 
becoming gradually denser as we approach the surface of 
the earth. If S B (fig. 3) represent a ray of light from 
a star, S, its course, after meeting the atmosphere at B, is 
bent more and more as it proceeds through the successive 



EEFRACTION. 



21 



atmospheric layers. The eye of the observer is only 
aware of the direction in which the light enters it ; so that 
the star is seen at T, or higher in the heavens than its 
real place. The amount of the displacement is not great, 




Fig. 3. 

unless the light comes in a very oblique direction. At 
the zenith (Z) there is no refraction, and all objects there 
appear in their true places. A star situated half-way 
between the zenith and the horizon (H 0) will appear too 
high by about Y, or the 30th part of the moon's diameter; 
but near the horizon, the light having to pass through a 
very thick as well as dense stratum of air, the amount of 
refraction is much greater, and its rate of increase very 
rapid.* At the horizon objects are raised by refraction 
about 33', from which it is clear that the sun or moon, 
whose diameters do not much exceed 30', are absolutely 
below the horizon at the time when they first appear to 

* Refraction varies very nearly as the tangent of the zenith 
distance ; and for all zenith distances less than 80° the following 
rule will give it pretty closely : — Refraction = 57" tangent zenith 
distance ; but since the density of the air depends to some extent 
upon its temperature and other causes, this is only to be con- 
sidered an average approximation. At greater zenith distances 
the rule fails. 



22 ASTRONOMY. 

graze it. Thus, when the sun is at N. (fig. 3), the light, 
having to pass through the atmosphere the whole distance 
from P to A, refraction is at its maximum, and the sun, 
to the observer at A, will be seen at M. 

A further effect of refraction upon the sun, when it is 
near setting, is to distort its figure very sensibly into a 
somewhat irregular oval. This is caused by the unequal 
effect of refraction upon the upper and lower margins of 
the sun, consequent upon its rapid increase near the 
horizon ; the lower margin being considerably more 
elevated than the upper, the sun appears compressed, or 
elliptical. It is to be remarked, also, that it appears 
larger when near setting than when high in the heavens. 
This is not caused by refraction, and indeed is only an illu- 
sion, as measures of its diameter made with the telescope 
will readily prove. Our ordinary ideas of the dimensions 
of objects are not simply obtained from their apparent 
size; we also take into account their distance, as well as 
we are able to judge of it. In judging the distance of the 
heavenly vault, that part near the horizon appears much 
more distant than near the zenith, partly because the 
dense stratum of atmosphere there subdues the brightness 
of its colour, producing the effect of distance, and partly 
because the eye is assisted in estimating by comparison 
with the features of the landscape. The want of objects 
for comparison deceives us in quite a similar manner, when 
we look across the sea at a distant ship, which, like the 
sky in the zenith, appears much nearer than it really is. 
We are thus doubly led by the imagination to fancy the 
sun more distant from us when setting than when high 
in the heavens, and hence attribute to it a greater size. 
The moon, although appreciably farther from us when on 
the horizon, and groups of stars, both in the same manner 
appear larger when nearly setting. 

Twilight is a phenomenon which also depends upon the 
atmosphere enveloping the earth. Every spot that was 
not directly in the sun's rays in the daytime, and the 
earth also, the moment the sun had set below the horizon, 
would otherwise be in profound darkness. This is abso- 



TWILIGHT. 



23 



lutely the case upon the moon, where there is no atmo- 
sphere sufficiently dense to be appreciable to us, as will 
be explained hereafter, and all shadows there appear 
perfectly black and sharply denned. The explanation of 
the existence of twilight, and the scattering of daylight in 
all directions, is found in the fact, that the air carries in it 
a large quantity of finely-divided dust, which we see in 
the sunbeam, and these minute solid particles have the 
property of reflecting light and diffusing it everywhere. 
Clouds also reflect and diffuse the solar light, as do doubt- 
less those minute particles of watery vapour which are 
always present in air in great quantity, and which some- 
times become visible as fog. 

The gradual fading away of this diffused solar light, 
which we call twilight, will readily be understood from 
the accompanying diagram.* 




Fig. 4. 



If an observer be stationed at N (fig. 4), RNS repre- 
senting the earth, H O k the stratum of atmosphere be- 
yond it, and H O the observer's horizon, the portion of 
atmosphere capable of diffusing light will be represented 

^ * The reader must be warned that, in order to show the effects 
of refraction, twilight, &c, in a diagram, those effects have to 
be greatly exaggerated. Thus, in fig. 4, if the earth be repre- 
sented by a circle of 2 inches diameter, that representing the 
atmosphere should only extend l-80th of an inch beyond it. 



24 ASTRONOMY. 

by the segment H N D, so long at least as the sun has 
not sunk below the horizon at P. When the sun is at 
M, the segment A m D will be illuminated by its rays ; 
but only that portion, ACOD, will be capable of giving 
reflected light to the observer at N. # Again, when the 
sun has reached K, the segment T> k Q will be wholly 
illuminated; but a still smaller portion, DOE, will 
reflect light to N". The twilight gradually fades to the 
observer, until the sun is about 18° below his horizon, at 
which time it becomes imperceptible. The duration of 
twilight at any place, therefore, depends upon the obli- 
quity of the sun's descent and the rapidity of his apparent 
diurnal movement. Within the tropics, where the daily 
course of the sun is never far from perpendicular to the 
horizon, twilight is always short ; but it is a mistake to 
suppose that there is no twilight near the equator. On 
the contrary, in this country and in others still further 
north, there is no night during a less or greater portion of 
the summer months, the sun never sinking so much as 
18° below the north horizon. It is to be noted that this 
limit is not invariable, but to some extent depends upon 
the meteorological state of the air ; twilight has been per- 
ceptible in this country, under certain atmospheric condi- 
tions, when the sun was as much as 21° below the horizon. 
Within the arctic and antarctic circles, twilight will con- 
tinue longer, and near the poles for days together. At 
the poles, the sun is above the horizon constantly for six 
months of the year ; and only two twilights, each of about 
fifty days' duration, would be experienced there. 

QUESTIONS. 

1. What proof of the earth's form do we obtain from the disap- 
pearance of objects at sea ? How do we know it is not the effect 
of distance only ? 

2. What is the Dip of the Horizon, and does it vary with the 
altitude of the spectator? 

* In consequence of the refraction of the sun's rays passing 
through the atmosphere, this is not strictly true. The atmosphere 
will be illuminated for a short distance further than the line / C 
upon the side of H. 



QUESTIONS. 25 

3. What is the amount of the earth's curvature in a mile, and 
where is this most readily seen ? 

4. Give other proofs of the earth's spherical form? 

5. Explain the mode of measuring a base line in trigonometrical 
surveys . 

6. Upon what base line does the triangulation of Great Britain 
and Ireland principally depend? Give the extremities of the 
meridional arc of England ? 

7. Where have the more important meridional arcs been 
measured, and what is discovered by a comparison of their 
results ? 

8. Where is the earth's curvature the greatest, and what figure 
results from the difference of curvature at the equator and the 
poles ? 

9. What are the exact dimensions of the earth? By whom 
determined ? 

10. Are these results confirmed by any other exact measure- 
ments ? 

11. Bound what point and in what figure are the diurnal 
motions of the stars performed ? 

12. Describe the motions of southern stars ? What alternative 
results from the motions of the stars ? Is their motion real ? 

13. Explain Foucault's pendulum experiment. What other 
instrument has M. Foucault devised to prove the earth's rotation ? 

14. What is the influence of the earth's rotation upon the 
weight of bodies at the poles and the equator ? 

15. How may this be determined experimentally ? 

16. What difference in the weight of a body results from these 
experiments ? Is this difference to be attributed wholly to centri- 
fugal force ? 

17. What proportion of the difference depends upon the form of 
the earth ? 

18. Give the lengths of a seconds' pendulum at Melville Island, 
Greenwich, and at the equator ? 

19. If the earth had been a perfect sphere, what would have 
been the effect of centrifugal force upon the waters on its surface ? 

20. What flattening would result from the earth's rotation, 
supposing it to have been a fluid mass of uniform density? 

21. State an argument in favour of the earth's rotation, derived 
from observation of other planets ? 

22. What are trade-winds ? and give the direction in either 
hemisphere ? 

23. How are trade- winds produced? 

24. Explain the cause of their easterly direction, and why this 
tendency is lost on approaching the equator ? 

25. How are cyclones produced ? 

26. What is their direction of rotation in either hemisphere, and 
how is this direction given to them ? 



26 ASTRONOMY. 

27. State the properties of atmospheric air that determine its 
distribution above the earth's surface ? 

28. Give the limit usually assigned as that of the atmosphere. 
Is its limit definite ? 

29. What instrument measures the weight of the atmosphere? 
At what elevation is the air only half the density at the sea- 
level? 

30. What is refraction ? What is the direction taken by a ray 
of light entering a denser from a rarer medium ? 

31. State the effect of atmospheric refraction upon the light of 
a star ? 

32. Where has atmospheric refraction no effect upon a ray of 
light, and where is it a maximum ? Illustrate this by its effect 
upon the setting sun ? 

33. Why does the sun appear oval when setting ? 

34. Why larger ? Give two reasons for this illusion 

35. What produces twilight ? Explain its gradual fading. 

36. How much is the sun below the horizon when twilight 
becomes imperceptible ? Is the limit invariable ? 

37. Where is twilight shortest ? Where longest? 

38. Has refraction any effect upon the duration of twilight ? 






27 



CHAPTER II. 

I. OF THE VARIOUS MODES OF DEFINING THE POSITIONS OF 
CELESTIAL OBJECTS. 

In order that the position of a heavenly body may be 
defined, two elements are necessary, precisely as two 
(latitude and longitude) are necessary in geography to fix 
the position of places upon the earth. We have the 
choice of several methods in astronomy ; but the simplest 
is to measure with proper instruments the height of the 
object above the horizon, and also, measuring round from 
the north point through the east, ascertain what angle of 
the horizon is included between the north point and the 
point where a perpendicular arc, let fall upon the horizon 
from the object, cuts it. In this case the horizon is said 
to be taken as the fundamental plane, and the two angular 
measurements, which are called co-ordinates, clearly fix 
the position of the object in the sky. The horizon is a 
great circle of the heavens, having for its poles the zenith 
and the nadir. The first is the point vertically above 
our heads ; the second that directly beneath our feet. 
The height of a star above the horizon is called its alti- 
tude, and the distance measured round upon the horizon 
from the north point is its azimuth. For some purposes 
this is a satisfactory way of fixing the place of a heavenly 
body ; but there are two reasons why its use is very 
limited. First, The position of the star, with reference 
to the horizon, is continually changing, in consequence of 
the rotation of the earth, and therefore the instant of ob- 
servation must be given also to fix the position. Secondly, 
The horizon itself changes with change of the place of 
observation, and this therefore requires to be given. 

A second system of co-ordinates, free from these incon- 
veniences, is obtained by taking the celestial equator, or 



28 ASTRONOMY. 

equinoctial, as the fundamental plane. The equinoctial 
is that great circle in the heavens midway between the 
poles, or it is very nearly the circle which the sun 
describes in its daily course upon the 20th of March ; or, 
again, it may be explained to be that circle in the heavens, 
formed by the plane of the terrestrial equator, produced 
infinitely in all directions. If the angular distance of a 
star north or south of the celestial equator is found, and 
the distance of the perpendicular to the equator from some 
starting point in it generally agreed upon, it will follow 
that the place of the star is satisfactorily defined. The 
perpendicular distance north or south of the equator is 
called the Declination, and the angular distance measured 
from the starting point along the equinoctial is called the 
Right Ascension. The advantage of this method is that 
the place of a star found by these co-ordinates remains 
permanent, neither depending upon the position of the 
observer nor the rotation of the earth ; but it is necessary 
to determine upon a desirable starting point. The bright 
star Altair, in the constellation of Aquila, was used at one 
time by some astronomers, in which case the reader will 
see a remarkable analogy between astronomical declina- 
tion and right ascension, and geographical latitude and 
longitude; but in more modern times the point of inter- 
section of two great circles (the equator and the ecliptic) 
has been universally taken as the origin of right ascensions. 
This point is called the First Point of Aries; but to explain 
the meaning of the term it is necessary that we should 
consider briefly the annual apparent motion of the sun. 

If we carefully watch the position of the stars for a 
number of nights in succession, we shall soon find that they 
do not occupy the same position in their diurnal circles of 
revolution at the same hour each night. If, for instance, 
we look out upon March 20th, as soon as the sun has set, 
which it does at this period of the year very nearly at 
6 p.m., the first star that is seen in the south is the 
bright star Sirius, the most conspicuous of all our stars. 
It will be first descried a little before 7 p.m., and will be 
very nearly due south. A week later it will be seen 



APPARENT ANNUAL MOTION OP THE SUN. 29 

decidedly to the westward at this hour of the evening, and 
a month later still it will be first descried not far from the 
western horizon. All the other stars will be seen to have 
the same westward motion, going always to meet the sun, 
and disappearing in his rays; while others rise from the 
eastern horizon to take their places, and to approach him 
in their turn. It amounts to the same thing to say that 
the sun has a motion from west to east, in opposition to 
the diurnal movement, and meets the stars. The rate of 
this motion is such that it makes an entire revolution 
round the earth in a year. (We are only speaking of 
apparent motions at present; it is of course the earth 
which revolves round the sun in the course of the year, 
but for the time we may assume the apparent motion to 
be real.) From March 20th, called the vernal equinox, 
because upon this day the sun is on the equator, making 
the day and night of equal length in all parts of the 
world, to June 21st, the sun performs a quarter of its 
annual course from west to east, and during this time it 
has also risen in the heavens to about 23^-° above the 
equator. Then it turns back again towards the south; 
and hence the circle over which it is vertical in its diurnal 
course upon this day is called the tropic (r^wa, I turn) 
of Cancer, the sun being in the constellation of that name. 
The point in the heavens which the sun occupies when it 
attains its greatest height is called the summer solstice 
(Sol, the Sun; Sto, I stand). After the next quarter of 
its annual course it reaches the equator on September 23d, 
and there is a second or autumnal equinox. Continuing 
in the same direction, it reaches its most southerly declina- 
tion (23|° south) on December 21st, called the winter 
solstice, the sun being in the constellation of Capricorn and 
vertical over the tropic of that name. After this it turns 
north, and arrives again at the vernal equinox on March 
20th, completing its entire revolution.* The apparent 

* This motion of the sun from south to north, and again from 
north to south, may be noted by the length of the noon-day 
shadow of a fixed object, from which the reader will obtain a 
much keener appreciation of the sun's movement than from mere 



t 
30 ASTRONOMY. 

motion of the sun round the earth is therefore in a great 
circle, cutting the plane of the equator at two points (the 
equinoxes), and inclined to it at an angle of nearly 23^°. 

This great circle is called the ecliptic, and the point of 
its intersection with the equator, which is taken as the 
origin or starting point of right ascensions, is called the 
First Point of Aries, because the sun enters that con- 
stellation at the vernal equinox, or on the 20th March. 
There is no star at this point of intersection to mark its 
place, but the frequent observation of the sun fixes the 
point with equal certainty; and we shall find further on 
that it is subject to a peculiar shifting along the ecliptic, 
which would make a fixed point in the heavens useless to 
mark its position for any length of time. 

A third system of co-ordinates in frequent use is 
obtained by taking the ecliptic as the fundamental plane ; 
and the angular distance of a body north or south of this 
circle, together with the distance of the perpendicular arc 
on it from the first point of Aries, similarly used as the 
starting point, will define the place of an object. The 
perpendicular distance of the object north or south of the 
ecliptic is called its latitude, and the angular distance, 
measured round the ecliptic from the First Point of Aries, 
is called its longitude. The student must be careful to 
distinguish astronomical latitude and longitude from the 
same terms used in geography, to which they have no 
resemblance but in name. It is much to be regretted 
that the same terms are used, but it is extremely difficult 
to alter an established custom. 

This svstem of co-ordinates is of great service in the 
discussion of the planetary motions, though observations 
of the places of all objects are made and expressed 
originally in the terms of the previously-mentioned system 
of co-ordinates. It is, however, quite easy, by the use of 
proper mathematical formulae, to convert the place of an 
object expressed in one set of terms to that in another. 

reading. It is much to be desired that, wherever it is practicable, 
the student will test the truth of our assertions by actual exami- 
nation of the heavens. 



DEFINING THE POSITIONS OF CELESTIAL OBJECTS. 31 




Fig. 



An example of the three sets of co-ordinates, with their 
respective planes of reference 
f and the mode of reckoning the 
several elements, is given in 
figs. 5 and 6. The observer is 
stationed on the earth at A, 
which may be supposed a point 
by comparison with the sphere 
of the heavens. H and O are 
the north and south points of 
his horizon, H h O o. P is the 
north pole of the heavens, Z the 
observer's zenith; the circle, 
HPZO, passing through these 
points is therefore the meridian of the place of observa- 
tion. S being a star, its altitude is represented by S M, 
and its azimuth by the large arc, Hh O M. The comple- 
ment of the altitude (Z S) is called the zenith distance. 
P and D being the poles, Wi Qo is the equator, the portion 
h Qo being above the horizon and visible to the observer. 
If C represent the first point of Aries, then the arc, 
C E o K, is the right ascension of the star S, and S K its 
north declination. The complement of the declination 
(S P) is called the polar distance. The spherical angle, 
S P Z, which represents the deviation of the star from the 
meridian, is called the hour angle. 

To prevent confusion, the horizon is omitted in fig. G; 
but the ecliptic, L E C F, is 
inserted, P' and D' being 
its north and south poles. The 
portion of the ecliptic, CEGL, 
is south of the equator; the 
remaining portion, C F L, is 
north. C is the first point of 
Aries, L the opposite point of 
intersection, sometimes called 
the First Point of Libra. The 
latitude of the star S is repre- 
sented by S G, and the longitude Tig. 6. 




32 ASTRONOMY. 

by the large arc, C F L G. The angle, Q C K, is the obliquity 
of the ecliptic, or its inclination to the equator (23^°). 
The first point of Aries occupies the position represented 
in fig. 6, about midnight in the beginning of August; and 
the student will be able to judge of the position of the 
ecliptic, with reference to the horizon and equator, at that 
time of the year from the diagram. The north pole of the 
ecliptic, it may be remarked, is situated nearly midway 
between two bright stars, o and £, in the constellation of 
Draco. The first pair of stars in the Great Bear, the well 
known pointers, indicate almost exactly the direction of 
the north pole of the equator, situated very near the pole 
star. The next pair of stars in the same constellation 
point with equal exactness to the north pole of the ecliptic; 
but the distance is rather greater. With this aid the 
position of the sun's annual path in the sky will be readily 
found. The great circle of the heavens that passes through 
both these poles and the solstices is called the solstitial 
colure; and another great circle at right angles to this, 
passing through the equinoxes, is called the equinoctial 
colure. 

II. OF THE INSTRUMENTS NECESSARY TO DETERMINE THE 
POSITION OF A HEAVENLY BODY. 

In speaking of the diurnal motions of the stars, we have 
said that they rise in the east, climb to a greater or less 
altitude, and then decline in the west. They all reach their 
greatest altitude, or culminate, when upon the meridian, a 
great circle of the heavens passing through the north and 
south points of the horizon and the zenith of the observer. 
When situated upon this circle, they are most favourably 
placed for observation, because least subject to displace- 
ment by refraction, which is always a doubtful element in 
the correction of astronomical observations. The Transit 
Instrument is designed to mark out this circle upon the 
sky, and to determine the right ascensions of objects as 
they culminate upon the meridian.* It consists of a 

* Originally invented by Eoemer, a Danish astronomer, about 
1681, A.D. 



ASTRONOMICAL INSTRUMENTS. 



33 



telescope mounted firmly upon a horizontal axis, the 
extremities being well turned cylindrical pivots, resting 
in metallic sockets upon massive stone piers. The reader 
will conceive the astronomical telescope to be simply a 




Fig 7. 



large lens or object-glass at O (^g. 7), which, gathering all 
the parallel rays of light that fall upon it from any object, 
causes them to converge so as to form a small inverted 
image of the object near the point F, which is called the 
focus. This image may be seen as a real object at the 
ordinary distance of clear vision (about 10 inches); and 
the earlier telescopes consisted of nothing more than this, 
the tube even being in some cases advantageously dis- 
pensed with. A simple microscope or eye-piece (V) was, 
however, soon added, by which the image was viewed and 
magnified, and the telescope was then comnlete. In the 
transit telescope a set of fine wires (usually of spider lines 
or silk) is inserted in the focus of the object-glass, which 

A. C 



34 



ASTRONOMY. 




rig. 



may be perfectly well seen through the eye-piece along 
with the object. The wires are generally five or seven in 
number, arranged as in fig. 8, with one horizontal wire to . 
mark the centre of the field. In 
order that these may be seen at night, 
the pivot and axis, P, is perforated, 
and the light of a lamp, L, is cast 
down the tube by an inclined annular 
reflector in the interior of the telescope 
at P. C is a graduated circle, and 
M a pointer or microscope, by the 
aid of which the telescope may be 
elevated to the meridian altitude of 
any particular star. 

In order that an instrument of this kind may truly 
sweep out the meridian by its revolution on the axis, P P', 
three conditions are necessary: — 1st. The telescope, or, 
more correctly, the centre ray of the cone of light formed 
by the object glass, which is called the line of colli- 
mation, or optical axis of the telescope, must be exactly 
at right angles to the axis of revolution, P P', otherwise 
a circle to the east or west of the true meridian, and 
smaller than it will be marked out. 2nd. The axis must 
be perfectly level, or the line of collimation will not pass 
through the zenith, though it may pass through the north 
and south points. 3rd. The axis must be placed due east 
and west, or the telescope will point to the zenith, but not 
to the pole, and therefore not to the north or south points 
of the horizon. Three errors, namely, of collimation, level, 
and azimuth, arise from the non-fulfilment of these con- 
ditions; and it is the duty of the practical astronomer to 
find out these errors and make allowance for their effects ; 
but it does not come within the province of the present 
work to explain the methods he employs in doing so. 
We may suppose the transit instrument perfect in its 
adjustments, the middle wire in its field coinciding with 
the line of collimation, and sweeping out accurately the 
meridian of the place of observation. 

An indispensable adjunct to the transit is a clock 



ASTRONOMICAL INSTRUMENTS. 35 

regulated so that it shall mark twenty-four hours in the 
time that a star performs its whole revolution from the 
meridian to its return to it upon the following day. This 
is rather less than an ordinary solar day — being only 
23 h 56 m 4*0 9 s of our ordinary time, and is, in fact, the 
time taken by the earth in making a complete revolu- 
tion on its axis. A clock so regulated is said to keep 
sidereal time, and requires to be so set that it shall mark 
h m s at the moment when the first point of Aries 
is upon the meridian of the place of observation. 

Suppose a clock so set and regulated, and the observer 
with his telescope is noting the passage of a star across 
the middle wire in the field,* it follows that the time 
occupied by the earth carrying the meridian of the observer 
from the first point of Aries to the star is shown by the 
clock; and since the earth's revolution is performed 
with perfect regularity, this is a true measure of the 
right ascension of the star expressed in time. If it is 
necessary to convert this to ordinary angular measure- 
ment in degrees, &c., we have but to multiply by 15, since 
the twenty-fourth part of the whole circumference, or 15°, 
is passed over in an hour. In this manner, then, one of the 
elements necessary to define the position of a heavenly 
body is found; the arc of the meridian between the star 
and the equinoctial is perpendicular to that circle, and 
the distance between the perpendicular and the first 
point of Aries has been measured by the time taken 
by the earth's revolution from the one point to the 
other. We have now only to measure the magnitude of 
this arc of the meridian to find the declination of the 
object, and its position upon the celestial sphere will then 
be known. 

The instrument used for this purpose is called the Mural 
Circle.t It consists of a telescope, A A, attached to a 
brass circle, and movoable with it upon an axis, C, run- 

* For greater accuracy, he notes the time of passage over each 
of the equidistant vertical wires, and takes an average or mean. 

t The Mural Circle is an improvement or extension of the mural 
quadrant, which was invented by the celebrated Tycho Brahe. 



36 



ASTRONOMY. 



ning th rough, the middle of a stone pier. The circle is 
placed in the meridian, in which plane it revolves, and 
its rim is very finely divided into degrees and other 
smaller divisions. Attached to the pier are microscopes, 
M M, usually from two to six in number, which act as 
pointers to ascertain the precise position of the circle. 




Fig. 9. 

The telescope is furnished with a horizontal wire in its 
focus, along which the star is made to pass, and the read- 
ing of the graduated circumference is noted. We have 
now to find the reading for the equinoctial; and had any 
conspicuous star been there, permanently marking it, we 
should only require to treat it in the same way, and take 
the difference of the two readings, which would be the 
declination. Instead of this, however, we may take the 
reading for the pole-star when on the meridian, which, 
being one of those northern stars that never set, but per- 
forms the whole of its diurnal circle above the horizon, 



ASTRONOMICAL INSTRUMENTS. 



37 



happens, twice each day, once above the pole and once 
below. Half-way between these two readings will be that 
for the pole itself, and 90° more will be that for the 
equator. The difference between this and the reading for 
the star is the declination of the star. 

Observations with the Mural Circle must be corrected 
for refraction; for which purpose elaborate tables are 
computed and published for every state of the atmosphere. 
In the case of planets and other bodies not far removed 
from the earth, a further correction is added, so that the 
results from all places upon the earth may be comparable. 
It is agreed to refer all observations of this kind to the 
centre of the earth, and to give the declinations as though 
observed there. The necessity for this will be seen from 
fig. 10. If S represent the place of a planet or other 
body, A and B two stations upon the earth, from which 
observations of 

- A \ 

I) 



it are made, 
and M m the 
sphere of the 
heavens, the 
observers at A 
and B will re- 
fer the object 
to the points 
F and D re- 
spectively. Th e Fig. 10. 
radius of the earth, A 0, being known, both observers 
can determine the direction of the line C E, or the 
position of the object as it would be seen from the centre 
of the earth. The immense distance of the stars renders 
such a correction quite unnecessary in their case. This 
is known as the correction for parallax. 

In modern observatories, it is not unusual to see a com- 
bination of the two instruments we have described, called 
a Transit Circle, which determines at once both elements. 
With either we have the means of measuring the positions 
of the heavenly bodies, and watching their motions from 
day to day ; but before we refer to any such observations, 




38 ASTRONOMY. 

it will be advisable to notice briefly one or two other 
astronomical instruments. 

III. EXTRA MERIDIONAL INSTRUMENTS — THE EQUATOREAL. 

The principal axis of this instrument is an inverted 
cone of metal, elevated so that the central line shall be 
parallel to the axis of the earth, or pointing to the 
celestial pole, and mounted upon a firm pedestal in such 
a manner as to be capable of revolving round the central 
line.* Near the upper extremity it carries a graduated 
circle at right angles to its length, and therefore parallel 
to the earth's equator, and in the plane of the equinoctial. 
Above this it carries a hollow cylindrical axis, also at 
right angles to the principal or polar axis, and both move 
round with it. Within this secondary or declination 
axis, a strong rod revolves, carrying at one end the 
telescope fixed in a cradle, and at the other a gradu- 
ated circle. Two motions, at right-angles to each other, 
may thus be given to the telescope. 1st, It may be 
revolved round the hollow axis, and be made to point 
successively to every degree of declination. 2nd, The 
polar axis may be made to revolve, carrying with it the 
whole instrument, and making the telescope point to each 
successive hour of Right Ascension. It may be turned, 
therefore, to any point in the sky; and if the declination 
axis is fixed, the simple motion of the polar axis will 
follow the course of any star throughout its diurnal circle, 
whether above or below the . horizon. This motion being 
perfectly uniform, it is easy to communicate it to the 
axis by clockwork, and is generally done with the advan- 
tage of leaving the observer quite free to make his 
observations upon objects for any length of time. The 
equatoreal is not usually employed in determining right 
ascensions and declinations, though these may be read off 
its two graduated circles, but rather the magnitudes, posi- 
tions, and distances of objects, capable of being seen in the 

* Equatoreals are variously designed : that described in the text 
is known as the Fraunhofer or German Equatoreal. 



EXTRA MERIDIONAL INSTRUMENTS. 39 

field of the telescope at one time. Very large telescopes 
are nearly always mounted as equatoreals. 

The Altazimuth, as its name implies, is used to measure 
the altitude and azimuth of objects. It is very variously 
designed, but generally consists of a massive graduated 
horizontal circle, capable of revolving on its centre, and 
supporting two vertical pillars, on the summit of which 
is carried a telescope lightly mounted, in a manner similar 
to a transit circle. Upon the horizontal circle the azimuth 
is measured, while the upper vertical circle serves to 
measure altitudes. Like the equatoreal, it turns to all 
points of the heavens, but is of greater steadiness than it. 
The results can rarely compete with those of the Transit 
Circle for accuracy, but in a portable form is of great 
service in determining the latitude of localities upon the 
earth's surface. 

Reflecting Telescopes. — The telescopes we have hitherto 
considered are all known as refractors, because the image 
viewed by the eye-piece is formed by the rays of light 
being refracted or bent from their previous direction by 
passing through a lens of dense glass, in obedience to the 
law explained in Chapter I. As originally constructed 
of a single lens of glass, they were defective, because the 
rays of coloured light, which together form white light, 
are not equally bent in passing through a dense medium 
such as glass. The images were therefore coloured, and 
this effect is said to be produced by the chromatic dis- 
persion of the lens. Many years afterwards (in 1747), 
Dollond, a London optician, corrected this fault, by unit- 
ing two glasses of different densities to form the object 
glass. Such telescopes are called achromatic refracting 
telescopes; but before this discovery the attention of 
Gregory, [Newton, and others was turned to devise a 
telescope upon a totally different plan. The principle of 
the reflecting telescope depends upon the fact that a concave 
mirror will form a perfect image of an object, provided the 
concavity is of the particular form known as a paraboloid 
of revolution. This figure does not differ much from a 
small segment of a sphere; and the point where the image 




40 ASTRONOMY. 

is formed is called its focus. Various methods are in use 
for viewing the image formed there; and hence telescopes 
are named after the original designers, as the Gregorian, 
Newtonian, Herschelian, and Cassegrainian reflectors. 
Fig. 1 1 is a section of the Newtonian telescope showing, 
by dotted lines, the direction of the rays of light after 

leaving the object. S 
is the speculum, or 
concave mirror; P, a 
y plane mirror, reflect- 
ing the light before it 
comes to the focus to 
the side of the tube, 
where it forms an 
image at L, which 
would otherwise have 
been formed at F. This 
Fig. 11. image is then viewed 

by the eye-glass at E. The speculum is of highly-polished 
metal, but does not reflect all the light that falls upon it? 
part is absorbed, but the image is free from colour, and 
in the hands of the elder Herschel almost superseded the 
refractor. The great telescopes of the Earl of Rosse are 
of this class; and, owing to the difficulty of polishing 
large glasses, more light can be collected with instruments 
of this class. After the discovery of the principle of 
achromatism by Dollond, refractors again came into 
favour, and, as instruments of precision, must continue to 
hold the first place. Quite recently, however, reflectors 
having glass speculum s, upon the surface of which silver 
is deposited and polished, have come into use, and, from 
their cheapness and excellence, bid fair — being mounted 
as equatoreals — to take a high place as extra meridional 
instruments. 

IV. MEASUREMENT OF TIME. 

One of the most important uses of the Transit Instru- 
ment, apart from the determination of Eight Ascensions, 
is the measurement of time. A day is always understood 



MEASUREMENT OF TIME. 41 

to be the interval between the departure from and return 
to the meridian of any celestial body. Thus, a solar day 
means the interval taken by the sun ; a lunar day, that 
taken by the moon ; and a sidereal day, that taken by a 
star. The solar day is evidently the most important to 
mankind in general, because on it depends the regular 
return of light and darkness, and at once suggests itself as 
the most obvious and natural unit of duration. The 
sidereal day is the most invariable unit, because the stars, 
being fixed and infinitely distant, the interval taken by 
them is precisely that taken by the earth in revolving 
on her axis; and this she does with so remarkable 
a steadiness of motion, that, from the record of ancient 
eclipses, we are able to discover that the length of 
the sidereal day has not varied so much as y^- of 
a second in more than two thousand years. As already 
stated, this interval is less than the ordinary mean 
solar day. The sun has an apparent motion in opposi- 
tion to that of the diurnal revolution of the stars, 
amounting to very nearly 1° per day; and when the 
rotation of the earth has brought again upon the meridian 
the point which was occupied by the sun the day before, 
that body is nearly a degree to the eastward, and nearly 
four minutes must elapse before the sun itself comes upon 
the meridian, and the solar day is completed. 

Secondly, the amount of the sun's apparent eastward 
motion is not the same each day. There are two causes 
for this : — 1st, Its actual movement depends upon the 
earth's motion in her orbit, which is sometimes quicker, 
sometimes slower ; and, 2nd, It is not performed in the 
equator, but in the ecliptic, which is considerably inclined 
to it. The solar day, at different times of the year, is not 
then of equal length ; and if it was used for the ordinary 
measurement of time, as it was in France before 1816, would 
lead to much confusion. A mean solar day is therefore 
used ; an arbitrary unit obtained by taking the average of 
all the solar days in a year. The difference between the 
apparent and the mean solar day is not great — never more 
than half a minute; but this, accumulating day by day, 



42 ASTRONOMY/ 

makes at times a great difference between the apparent 
and mean noon. Thus, upon September 1 the mean and 
apparent noon coincide; but the solar day being at this 
time shorter than the mean solar day by nearly half a 
minute, at the end of the month the sun passes the meri- 
dian ten minutes before the mean noon arrives. This 
difference is known as the equation of time, and attains its 
greatest magnitude about November 1, when the sun is 
more than sixteen minutes before the clock keeping mean 
time. On December 24, the sun having been moving 
faster in the heavens, the mean and apparent noon coin- 
cide again, and there is no equation of time on that day; 
but the sun's motion still continuing fast, on February 11 
the sun does not pass the meridian till 14 J minutes after 
the clock has indicated mean noon. On four days of the 
year the mean and apparent time agree, and there is no 
equation of time ; twice the sun reaches a maximum in 
advance of the clock, and twice also behind the clock. 

The expression mean sun is often found in astronomical 
books. By it must be understood an imaginary sun, that 
in a year shall be found to have moved at the same pace 
as the real sun, but uniformly day by day, and in the 
equator ; a sun, in fact, that shall always agree with our 
mean time clocks. 

Since the sun is only on the meridian of a given place 
at a given time, the noon of all places situated east or west 
of each other must vary, and with it the local mean time 
of all such places, since noon is its starting point. In 
Britain the time of Greenwich is everywhere kept; but 
before the introduction of railways the local time at each 
place was usually kept there. The City of Oxford was 
the last town of importance to adopt Greenwich in place 
of local time. In large towns on the continent it is usual 
to keep the time of the metropolis of the country, but this 
is not invariable. The difference of longitude of any two 
places expressed in time (i.e., the ordinary longitude divided 
by 15) will give their difference of local time, the more 
eastern station being of course the later. 

For a longer unit the duration of the earth's revolution 



MEASUREMENT OF TIME. 43 

round the sun is employed. The time that elapses from 
the moment of the sun leaving a particular star to its 
return to it is called a sidereal year, and is equal in 
mean solar time to 365 days 6 h 9 m 9*35 s ; or, in sidereal 
time, to 366 days 6 h 9 m 9*35 s . A more generally impor- 
tant measure of the length of the year, however, is 
determined by the time that elapses between the sun's 
departure from and arrival at the equinox. This is called 
the tropical year. We have already alluded to the fact 
that the equinox is not a fixed point in the heavens, like 
a star, and the slow movement of it occasions the year, 
which depends upon the sun's arrival at this point, to 
be less than the sidereal revolution of the earth by 
20 m 23'2 S , or to amount to 365 days 5 h 48 m 46*15 s of 
mean solar time. Upon this period depends the return 
of the seasons, since they commence with the arrival of 
the sun at the equinoxes and the solstices, and it is there- 
fore the year which it is necessary to employ in framing 
the calendar. Obviously it is desirable that our seasons 
should commence upon the same day of the year as they 
did in the most remote times ; and as only a slight error 
in the assumed length of the year would throw us out 
considerably after the lapse of some centuries, the arrange- 
ment by which an exact number of days are assigned to 
each year is a matter of much consequence. Previous to 
the time of Julius Caesar (b.C. 44) much uncertainty pre- 
vailed in this respect; but, as arranged by him, the year 
was to consist of 365 days, and every fourth year was 
bissextile, or consisted of 366 days. This amounted to 
assuming the tropical year equal to 365^ days ; but since 
it is not so much as this by fully 11 minutes, the 
calendar is not sufficiently accurate. It was found that 
from the time of the Council of Nice (a.d. 325), when 
Easter was ordered to depend upon the vernal equinox, to 
the time of Pope Gregory XIII. (a.d. 1582), the Julian 
calendar had lost ten days, or the vernal equinox, and with 
it the seasons were ten days earlier in the year in a.d. 1582 
than they were in a.d. 325. Pope Gregory corrected 
the error by advancing the date ten days, and decreed that 



44 ASTRONOMY. 

the first year of every century, unless divisible by 400, 
should be an ordinary year of 365 days, instead of a leap 
year. This arrangement so very nearly agrees with the 
length of the tropical year that the seasons now retreat 
only one day on the calendar in four thousand years, which 
is sufficiently near the truth for all practical purposes. Even 
this may be corrected, if it is deemed necessary, at the 
expiration of that interval. 

The improved or Gregorian calendar was not introduced 
into England until the year 1752, at which time the 
seasons had advanced eleven days on the Julian calendar. 
Subsequently the reckoning is known as the jSTew Style, 
in opposition to the Julian or Old Style ; and to convert 
the Old into the New it is only necessary to add eleven 
days to the date. Thus, 1749, April 12, O.S., is equi- 
valent to 1749, April 23, JST.S. The beginning of the 
year was, however, at the same time altered from March 
25 to January 1, so that to convert Old Style into New, 
when the date falls between these, it is necessary to add 
one year also ; thus, 1748, February 5, O.S., is equivalent 
to 1749, February 16, N.S. In Russia the Julian calen- 
dar is still in use, the difference being now twelve days. 

QUESTIONS. 

1. What is meant by the term co-ordinates ? 

2. Explain the terms zenith, nadir, altitude, and azimuth. 

3. Why are the co-ordinates having the horizon as a funda- 
mental plane generally unsatisfactory ? 

4. What is the equinoctial ? Explain the terms declination and 
right ascension. 

5. What point is used as the origin of right ascensions, and 
of what great circles is it the intersection? Is it a fixed point? 

6. Describe the apparent motion of the sun among the stars. 
What is the ecliptic ? 

7. Over what parts of the earth is the sun vertical at the sol- 
stices, at the equinoxes ? Explain these terms. 

8. What is meant by astronomical longitude and latitude, and 
for what are these co-ordinates principally used ? 

9. Explain the terms meridian, hour angle, first point of Libra, 
obliquity of the ecliptic, solstitial colure, equinoctial colure. 

10. With what instrument are right ascensions determined? 
Describe it. By whom and when invented ? 



QUESTIONS. 45 

11. Explain the construction of the astronomical telescope. 

12. What are the conditions under which a transit instrument 
will revolve accurately in the meridian ? 

13. To what errors is the transit instrument subject from 
improper adjustment ? 

14. Explain what is meant by sidereal time. When a sidereal 
clock marks noon, what point is on the meridian? 

15. Describe the mural circle. For what purpose is it used? 

16. How may the circle reading of the equinoctial be found? : 

17. What corrections have to be made to mural circle observa- 
tions? 

18. Describe the equatoreal. What are the directions of its 
two axes? What advantage is derived from the elevation of the 
polar axis ? 

19. Describe the altazimuth. What are its advantages over the 
equatoreal ? For what purposes is it mostly used ? 

20. What is chromatic dispersion, and from whence does it 
arise ? How is it overcome ? 

21. State the principle of reflecting telescopes. Describe the 
arrangement of mirrors in the Newtonian reflector. 

22. What is meant by a day ? What is a sidereal day ? a solar 
day ? Why is the solar day longer than the sidereal? 

23. Why is the solar day an unsatisfactory unit of time ? Ex- 
plain the reasons of the variation in the length of the solar day. 

24. What is a mean solar day, and how often in the year does 
mean solar time and apparent solar time coincide? 

25. Give the greatest differences between mean and apparent 
solar time, with the days on which they occur. 

26. What is the equation of time, and what is meant by the 
term mean sun ? 

27. Give the cause of difference of local mean time, and the rule 
fcr finding the local time at any place whose longitude is given. 

28. What is meant by a sidereal year ? What is its duration 
in mean time? in sidereal time? 

29. What is meant by a tropical year? Give its duration. 
Why does it differ from the sidereal year ? 

30. Explain the Julian calendar, and give the reason of its 
inaccuracy. By whom, how, and when was it corrected ? 

31. Explain the new and old style, and the mode of converting 
the one to the other. 



46 



CHAPTER III. 

I. LAWS OF PLANETARY MOTION. 

A careful scrutiny of the heavens for a number of 
nights reveals the fact that there are other bodies than 
the sun having independent motions. The moon in only 
a few hours shows a very rapid and palpable movement, 
and a few bright objects, which we call planets (-z-Aai/^T^, 
a wanderer), are also detected to have very considerable 
motions of their own. If we confine our attention at 
present to the planets, we shall find their movements 
very various and intricate. Venus and Mercury will be 
found always near the sun, sometimes on the east, some- 
times on the west of him. Ordinarily they are seen 
travelling in the same direction as the sun, or in opposi- 
tion to the diurnal movement of the stars. This 
is called direct motion. At times they become sta- 
tionary, and then turn back in the opposite direction, 
at which time their motion is called retrograde. Again, 
they will become stationary, and afterwards resume their 
previous direct motion. The other planets, Mars, Jupiter, 
and Saturn, which are conspicuous objects, will be seen 
to have similar motions, though they do not remain in 
attendance upon the sun. The five planets already men- 
tioned were known to the ancients, who watched their 
motions with great interest, and formed numerous expla- 
natory theories. In spite of all their ingenuity, and their 
intricate systems of epicycles and differents, their theories 
would not agree with the observed planetary motions. 
They were entirely vitiated by one erroneous assumption. 
The magnitude and importance of the earth to themselves, 
led them always to fix upon it as the centre of the uni- 
verse, around which moved the sun and planets with the 
most intolerably complicated movements. The system 



LAWS OF PLANETARY MOTION. 47 

which endeavours to explain these motions, on the sup- 
position of the earth being fixed, and the centre of their 
revolutions, was invented by Hipparchus, but is generally 
known as the Ptolemaic system, after the celebrated 
astronomer who advocated it ; and the difficulty of propa- 
gating any other, in the face of the popular ideas, caused 
the most profound darkness to prevail for many centuries. 
Pythagoras, it is true, and one or two others of the ancients, 
are known to have held more correct notions, but were 
unable to impress them upon their disciples. Early in 
the sixteenth century, Nicholas Copernicus, a monk of 
Thorn (Polish Prussia), revived the theory of Pythagoras 
by placing the sun in the centre of the universe, with the 
planets and the earth revolving round him ; but though he 
thereby considerably simplified the theory, and had hit 
upon the true explanation of the complex planetary 
motions, he could not account for them accurately without 
some remnants of the old Ptolemaic theory. But very 
shortly after his time observational astronomy advanced 
rapidly, and the laborious life-long work of Tycho Brahe, 
together with his ingenious methods of observation, put it in 
the power of his successor, Kepler, to devise a theory which 
should rigorously account for the motions of the planets. 
Gifted with the most daring imagination and unwearied 
energy, this illustrious philosopher tried every possible 
assumption upon which to explain the positions of the 
planet Mars, as observed by Tycho and himself, upon the 
theory of a central sun with circularly revolving planets, 
but without success. For seventeen years he laboured, 
and finally found it possible to account for all the motions 
of the planets upon the supposition of their being 
governed by three simple laws, which we now know to be 
the true solution of this most troublesome problem. They 
are known as Kepler's laws, and are as follows : — 

1st. The planets revolve in ellipses around the sun, of 
which it occupies one of the foci. 

All the previous endeavours had aimed at the explan- 
ation of the phenomena upon the assumption of uniform 
motion in circular orbits. Next to the circle the ellipse is 



48 



ASTRONOMY. 



the simplest geometrical figure. It is obtained by cutting 
a cone in a direction oblique to its base, and may be 
defined to be an oval figure, within which are two points, 
called foci, the sum of whose distances from any point In 
the curve is always the same and equal to the longer axis. 
From this will be understood the ordinary method of 
describing an ellipse — namely, to fasten the extremities of 
a loose thread to a board, and describe a curve with the 
string always stretched by the pencil. 




Fig. 12. 

Fig. 12 represents the orbit of a planet. S, the sun 
situated in one of the foci. F is the other or unoccupied 
focus of the ellipse. A P is called the major, and M N" 
the minor axis. P, the point at which the planet is 
nearest to the sun, is called the perihelion of the orbit. 
A, the point where it is most distant, is called the aphelion. 
Any line joining the sun to the planet, as SR, S Y. is 
called the radius vector of the orbit. C is the centre of the 
ellipse, and C A the semi-axis maj or, or mean distance. The 
eccentricity of an ellipse is its deviation from a circle, and 
is expressed by the ratio of C S to C P. In the case of 
the planets, the eccentricity is very small, the orbits 
not differing much from circles. The angle, CMS, 



LAWS OF PLANETARY MOTION. 49 

called the angle of eccentricity, is likewise small.* The 
line A P, which is the major axis of the ellipse, is fre- 
quently called also the line of apsides. The angular dis- 
tance of a planet from perihelion is called its true anomaly, 
and that of the point it would have reached with uniform 
motion its mean anomaly. The difference between them 
is the Equation of the Centre. 

2nd. Kepler s second law, which is also known as the 
law of conservation of areas, is usually enunciated in the 
following terms : — The radius vector in any orbit sweeps 
over equal areas in equal times. If, then, the areas SEV 
(fig. 12), Svr, and Mw S are equal to one another, it 
follows from this law that the planet will describe the 
arcs HV, vr, and v M in equal periods of time, and that 
hence its velocity is greater according as its distance 
from the sun is less. "We have thus the means of tracing 
the position of a planet in its orbit ; but it must be remem- 
bered that the areas swept over by the radius vector of 
one planet have no relation to those of another planet, 
which may be either greater or less. 

The 3rd and most important law of Kepler, has refer- 
ence to the periodic times and the distances of the planets 
from the sun. He discovered that the squares of the times 
of revolution of any two planets have the same proportion 
to each other as the cubes of their mean distances have; from 
which it follows that, having once found the distance of 
any one planet from the sun, a simple proportion will 
enable us to fiud the distance of any other. As enun- 
ciated above, this law is not strictly true, but very nearly 
so, owing to the mass or weight of the planets being 
almost inappreciable by comparison with that of the sun. 

The same law regulates the times and distances of 
moons or secondary planets ; but these are not always 
insignificant in comparison with their primaries, and their 
mass requires to be taken into account in the calculation. 
The first and third of these laws are consequences of the 

c s 
* M S being equal to C P, the eccentricity — is the natural 

sine of the angle of eccentricity, CMS, 

A. i) 



50 



ASTRONOMY. 



universal law of gravitation, which we shall explain in the 
next section; the second has been proved by Newton to 
follow from the simple laws of motion, having no connection 
with the theory of gravitation further than proving the sun 
to be the centre of attraction for each of the planets. 

To complete our view of planetary orbits, we have only 
to add that they lie very nearly in the plane of the ecliptic, 
yet a little inclined to it, and hence the planets are 
always found in a narrow zone of the heavens, known as 
the Zodiac. Fig. 13 is a perspective view of the orbits of 
the Earth and Yenus, from which it will be seen that the 




Fig. 13. 

orbit of Venus cuts the plane of the earth's, or the 
ecliptic, at two points, N n. These are called the nodes 
of the orbit. At one of them Yenus will rise from the 
south to the north side of the ecliptic — hence called the 
ascending node ; at the opposite point the reverse will 
happen, and it is therefore called the descending node. 
The line joining the nodes, which necessarily passes through 
the sun, is called the line of nodes. 

The various parts of an elliptic orbit having now been 
described, we are in a position to point out what it is 
necessary to know in order to follow the motions of a 
planet in her orbit, or in the heavens. 1st. The form 
and magnitude of the ellipse must be known — that is to 
say, its eccentricity and the length of the semi-axis 
major. 2nd. The position or longitude of the planet 
must be known at some particular time, and its mean 
daily orbital movement. 3rd. The position of the plane 
in which the orbit lies must be known — that is, its in- 
clination to the ecliptic, and the longitude of the ascending 



r' 



THE UNIVERSAL LAW OF GRAVITATION. 51 



node ; and, Uh. The position of the ellipse in that plane 
must be known, or the longitude of the perihelion. 
These are called the elements of the orbit; and once found, 
the position of the planet can either be calculated in 
advance or carried back into the past. 

II. OF THE UNIVERSAL LAW OF GRAVITATION. 

Although it would be possible, by the aid of Kepler's 
laws alone, to follow the movements of the planets pretty- 
closely, yet, being derived as they are from observation, 
they afford us no information as to the principle that 
gives them birth. They do not explain why the planets 
move in ellipses, nor why the distances and periodic times 
of the planets should bear such a relation to each other 
as they do. They are not, in fact, of that simple and 
ultimate character in which it is usual to find the laws of 
nature capable of being expressed. Newton was first led 
to conjecture whether the attractive force that keeps the 
moon in her orbit round the earth, might not be the same 
as that which causes all bodies on the earth's surface to 
tend towards her centre. This force, which we call 
gravitation, we know extends to the greatest altitudes 
which it is possible for us to reach ; and since there is no 
reason why we should set a limit to its power at any 
definite distance from the surface of the earth, it is 
feasible to suppose that it may possibly extend as far as 
the moon. The revolving motion of the moon in her 
orbit must generate a centrifugal force; and there must 
always be in consequence a tendency in the moon to fly 
off in the direction in which she is at the moment 
travelling, or of the tangent to her orbit. This is in 
obedience to the first law of motion, which states that if 
a body be put in motion in any direction it will continue 
to move for ever in that direction, and with the same 
velocity, in a straight line, unless deflected from it by the 
action of some other force. Now, to measure the moon's 
distance is a very simple question, as we shall see shortly; 
and it was well known by Newton to be sixty times the 



52 



ASTRONOMY. 



earth's radius. Its time of revolution was also known, so 
that the amount of centrifugal tendency was calculable. 
The moon, however, does not move in a straight line, a 
tangent to her crbit; and it is therefore clear that there 
must be some other force precisely equal in effect that 
continually draws her towards the earth; because if this 
attraction of the earth were less than the centrifugal 
tendency, the moon would increase her distance; and if 
greater, she would be drawn towards the earth. The 
amount of the attractive force that the earth is constantly 
exerting on the moon is expressed by the distance through 
which the moon is drawn from the straight line in any 
given time. This is agreeable to the second law of 
motion, which is to the effect that, when two forces 
are acting upon a body so as to produce motion, the 
body will be found, after a given interval, at that point 
which it would have occupied supposing each to have 

acted upon it separately. Thus, in 
figure 14, if M C represent the dis- 
tance which the moon would travel 
in a given time, supposing gravity to 
have no effect, and M G the distance 
through which the moon would be 
drawn by the effect of gravity, sup- 
posing it to be acted upon by no 
force impelling it in any other 
direction, then the point it will 
actually reach in the given time, 
both forces acting upon it, will be 
the point m, after describing the 
arc M m. C m being equal to M G 
measures the amount of the attract- 
ing force of the earth, which may be 
found in feet, and compared with 
the force of gravity at the earth's 
surface — i. e., with the distance 
through which a stone would fall 
Fig. 14. near the surface in an equal period 

of time. In this way Newton found that, supposing 




THE UNIVERSAL LAW OF GRAVITATION. 53 

gravity to be the force that deflects the moon from C to m, 
and counteracts the centrifugal tendency of the moon, 
forcing it into a curvilinear orbit, it must be enfeebled 
by the distance of the moon to 86 1 00 part of what it is at 
the surface of the earth, or that it diminishes in the same 
proportion as the square of the distance (3,600 = 60 2 ) 
increases. Nor is this an extraordinary result, because 
both light and heat, which are natural emanations from a 
centre, do diminish with distance in this precise propor- 
tion ; and analogy would lead to a similar supposition in 
the case of gravity. 

Now, supposing this to be the rate of diminution of the 
force of gravity, it is necessary to show that Kepler's laws 
flow from it before we can assume that the actual force 
which retains the planets in their orbits is none other 
than gravity. This Newton has done by proving, first, 
that the motions of all bodies must, under the law, as he 
has enunciated it, be some one of the curves known as 
conic sections.* In other words, that bodies moving 
round the sun must either move in a circle or an ellipse, 
of any degree of eccentricity, or they may follow the 
curves known as the parabola and the hyperbola, in 
which last cases they do not return to the sun after having 
once passed round it. Of each of these curves we find 
examples in the Solar System. The planets revolve in 
ellipses of small but various eccentricities, while some 
comets have elliptic orbits of very great eccentricity. The 
satellites of Jupiter revolve in circles. The majority of 
comets move in parabolic orbits, while in some the 
hyperbola is the form assumed. 

* The four curves — the circle, parabola, ellipse, and hyperbola — 
are called conic sections, for the reason that when a cone is cut by 
a plane surface, other than through the apex, the boundary of the 
intersection will be one or other of these curves. If the cone be 
cut parallel to the base, the section will be a circle ; if cut obliquely 
parallel to the side of the cone, the section is a parabola. If the 
cone is cut across in any other direction than parallel to the base, 
the boundary will be an ellipse; and in every other section, as per- 
pendicular to the base, for example, the form of the boundary will 
be a hyperbola. 



54 ASTRONOMY. 

He further proved that the law of the distances and 
the periodic times would be a consequence from the 
extension of gravitation under this form to the planets ; 
while the second of Kepler's laws he proved to follow 
likewise, without the application of the particular ratio of 
diminution which gravity follows. He was therefore led 
to give the widest signification to this law, which we will 
now state in its fullest application : — 

Every particle of matter in the universe attracts every 
other particle, with a force varying directly as the mass of 
the attracting particle, and inversely as the square of the 
distance between them. From which it will be seen that, 
should the earth from some cause be increased to twice 
its weight or mass, then the force of gravity which it 
exerts upon the moon would be increased twofold; or, 
further, should its mass remain the same, and the dis- 
tance of the moon be reduced to one -half its present 
distance, then the force of gravity exerted by the earth on 
the moon would be four times what it now is. 

That the true secret of the planetary motions was pene- 
trated by Newton, and is expressed in the few simple 
terms above, does not rest alone upon the explanation 
which it affords of the origin of the Laws of Kepler, but 
in its wide application to the whole theory of the heavenly 
motions. Every slight deviation from a strictly defined 
ellipse must be explained as some effect of the general 
application of the Newtonian law ; and should it fail in 
any single instance, it would at once fall to the ground. 
It has been found, however, perfectly sufficient to explain 
every movement and every minute variation, while some 
slight deviations have even been first detected by theory, 
and afterwards confirmed by observation. Newton was 
fully alive to the wide consequences of this extensive 
generalization. If the earth attracts the moon, it in 
its turn also attracts the earth; while the sun attracts 
both with an ever varying force, conforming to their 
ever changing distances. The planets also disturb the 
earth and her moon, which also disturb them in their 
movements. In this manner very many minute disturb- 



THE UNIVERSAL LAW OF GRAVITATION. 



55 



ances arise affecting every member of the Solar System, 
called perturbations, and it often requires tl e highest 
powers of the mathematician to trace these to their 
sources and to calculate their amounts. Of some of the 
more important of these we shall treat in a later chapter. 
There are one or two points to which we must call the 
student's attention before leaving this part of the subject. 
First, that the attraction of spheres — and the earth is 
very nearly, though, not quite, a perfect sphere — is pre- 
cisely the same as if all the matter composing it had been 
collected at the centre, and we are therefore situated at a 
distance of the earth's radius from the centre of attraction. 
This fact was likewise proved by Newton, and it explains 
why any altitude which we can reach makes no appreci- 
able difference in the effect of gravity; for we can only 
add a very small fractional part of the earth's radius to 
our present distance from the centre of attraction. 
Secondly, that since the earth does deviate slightly from 
a strictly spherical form, the direction of the plumb-line, 
which is towards the centre of attraction, differs by a 
small amount from the direction of the earth's centre. 
Thus, in fig. 15, we 
have the elliptic 
form of the meri- 
dian circle greatly 
exaggerated to show 
this difference. HO, 
the tangent at the 
point A, is the ob- 
server's horizon; Z 
is therefore his 
zenith ; and A Z 
the direction of the 
plumb-line. A Z' 
is the prolongation 

of the radius of the Fig. 15. 

earth at the point A. The small angle, Z' A 
deviation of the plumb-line from the direction 




earth's centre — is called the angle of the vertical. 



Z— the 
of the 
At the 



5£ ASTRONOMY. 

equator, or at the poles, there is no such angle, and it is 
always small, owing to the near approach of the meridian 
to a circle. In the latitude of Greenwich, it amounts to 
only 11 J minutes of arc. A P" being the direction of 
the celestial pole, and A Q' of the equinoctial, the angle 
Z A Q' is the apparent or geographical latitude ; Z' being 
the geocentric zenith, the angle Z' A Q' is the geocentric 
latitude; their difference being the angle of the vertical 
at the point A. Thirdly, that in an elliptic orbit, the 
motion being greatest when the planet is in perihelion, 
or nearest the sun, the centrifugal force is greatest also, 
and the greater attractive force of the sun is as much 
counterbalanced at that point as at any other ; while the 
great velocity acquired after passing perihelion enables 
the planet to draw away from the sun — a fact which some 
people have difficulty in apprehending. This balancing 
of forces is the great element of stability in our system ; 
for, should any accident increase the sun's gravity, it would 
merely force the earth and other planets into different 
orbits, and in no way tend to precipitate them upon the 
sun. Lastly, that treating the earth as we have already 
treated the moon, by computing its centrifugal force in 
its orbit round the sun, we have the means of weighing 
that body against ourselves; but in order to do this it is 
necessary that we should be acquainted with the distance 
of the sun from the earth — of which problem we shall treat 
in the ensuing section. 

nr. PARALLAX. 

The term parallax, as used in astronomy, implies the 
difference in the direction of an object as seen from two 
different points, without defining what those two points are. 
We have seen that the correction for terrestrial parallax 
in mural circle observations is a quantity varying with 
the distance of the object and its altitude, subtracted from 
the zenith distances of all objects not infinitely remote, in 
order that the results may be such as would have been 
obtained at the centre of the earth, supposing it possible 



PARALLAX. 



57 



to have a mural circle stationed there, the point to which all 
the observations of the various observatories are referred. 
The distance of the moon is found in a very simple man- 
ner. Two observatories, duly supplied with mural circles, 
are selected as nearly as possible in the same meridian, 
but differing greatly in latitude — as Greenwich and the 
Cape of Good Hope. If G E C (fig. 16) represent the 




Fig 16. 

earth, G and C being the selected stations, G P and C P', 
the elevation of the north and south pole of the heavens 
at either station; then, if the moon, M, were infinitely 
remote, the sum of the angles, PGM and P' C M, the 
polar distances as measured at the two stations (cleared of 
refraction), would be two right angles, or 180°; but the 
moon being comparatively near, their sum will exceed 
180° by the angle G M C,* which is the parallax of the 
moon at the station G (viz., L M G), together with the 
parallax at station C (viz., C M L). The proportion of 
the excess, or the parallax at each station, must then be 
assigned; and hence the value of G M L, of L G M 
(altitude of moon at G + 90°), and the radius L G are 
known. The length of the side, L M, or the distance of 

* If the stations are not on the same meridian, a correction must 
he made for the change of Polar Distance of the moon while passing 
from the one meridian to the other. 



•38 ASTRONOMY. 

the centres of the earth and moon, will be found by the 
application of the principles for the solution of triangles. 

It will be seen that parallax must be greatest when 
G M coincides with GO, or when the object is on the 
horizon ; it will further be slightly larger if L G is an 
equatorial radius, so that the equatorial horizontal parallax 
is the maximum parallax. At the moon's mean distance 
this amounts to 57'" 2"* 33, corresponding to an average 
distance of 60^ times the equatorial radius of the earth, or 
about 238,851 miles. 

When the parallax of an object is mentioned apart from 
any particular place or altitude, the maximum or equa- 
torial horizontal parallax is to be understood — that being, in 
fact, none other than the angle which an equatorial radius 
of the earth subtends at the distance of the object; and if it 
is found, the distance of the object in miles is obtained by the 
solution of a right-angled triangle, of which all the angles 
and one side (viz., the earth's radius) are known. Indeed, 
astronomers rarely express distances in miles, the equato- 
rial horizontal parallax being much more simple and easy 
to deal with, while the actual distance is so readily found 
from it, if wanted. 

To obtain the parallax and distance of the sun is a 
problem of greater complexity, and for a long time baffled 
the earlier astronomers, so that even Kepler, who knew 
accurately the relative distances of all the planets from the 
sun, was quite ignorant of the actual distance of any one 
of them. It might have been obtained in a similar manner 
to that of the moon; but the. solar parallax is so small an 
angle, and the heat of the sun has such a disturbing effect 
upon atmospheric refraction, that the result would be very 
far from reliable. Another method which was known to 
the ancients, and even attempted by Aristarchus of Samos, 
would have led to a fairly accurate result, had the moon's 
surface been less rugged than it is. It consists in measuring 
the angular distance between the centres of the sun and 
moon at the time when the latter is dichotomized — that is, 
when exactly one-half of it is illuminated by the sun. At 
this moment the line joining the earth and moon must 




PARALLAX. 59 

form, with that joining the moon and sun, an exact right 

angle (see fig. 17); and if the 

distance of the moon is known, 

and the angle between the sun 

and moon as seen from the earth 

(viz., M E S), measured, we have 

all that is necessary to solve the 

right-angled triangle, M E S, Fig. 17. 

and to find the sun's distance, E S. 

But since both these methods fail, we are obliged to 
take advantage of the phenomenon of a transit of the 
planet Venus across the sun's disc, which happens occa- 
sionally at rare intervals. It will be seen from fig. 13 
that if the earth happens to be at the point n of her orbit, 
when Venus is at or near her node, the planet will be seen 
projected as a black spot upon the sun, the three bodies 
being in a straight line. The same may happen at the 
opposite node, but at no other position in the orbit of 
either. This occurred in 1761 and 1769, and will occur 
again in 1874 and 1882. The intervals being alternately 
8 and 105| years, and 8 and 121 \ years, transits will 
not take place after 1882 till the years 2004 and 2012. 
The reason why there are two transits at a short interval 
is, that thirteen revolutions of Venus are very nearly equal 
to eight revolutions of the earth; and hence, after eight 
years, the planets occupy nearly, but not quite, the same 
positions with reference to the nodes as at first. Yet, 
after the lapse of eight years more, Venus will be too far 
from the node for a transit to take place, and a long inter- 
val elapses before the planets are similarly situated at the 
opposite node. 

If a transit is viewed at two widely distant places on 
the earth, whose distance will be known from its dimen- 
sions, the planet will be seen to occupy different positions 
on the sun's disc. Let C and F (fig. 18) be "the two 
stations, supposed, for the sake of simplicity, to be 
situated at opposite extremities of the earth's diameter, 
and V the planet Venus, the points at which Venus will 
be seen projected upon the sun are c and / respectively, 



60 



ASTRONOMY. 



the transits taking place along the lines & c" and/ f". 
The duration of the transits or other means may be 
employed to measure the breadth of the zone, C c" f f", 
or the line cf. Now, from Kepler's third law, we know 




Fig. 18. 
the ratio of the distances of Venus from the earth 
and sun to be that of 28 to 72; and since the ratio 
between C F and c/will be the same, the actual length 
of c f is found in this manner, being |-|, or nearly 2 \ 
times the earth's diameter, or five times its radius. The 
angular measure of the radius of the earth at the distance 
of the sun is the solar parallax, and the angular measure 
of cf is, therefore, five times the parallax. Hence the 
distance of the sun is at once found. 

Observations were made for this purpose at the sugges- 
tion of Halley in 1761, and more successfully in 1769. 
From the latter observations a parallax of 8"*5776 was 
determined, corresponding to a mean distance of 95,300,000 
miles. Since that date this has been assumed, not only as 
the distance of the sun, but as the scale by means of 
which, and Kepler's third law, the whole of the dimensions 
of the solar system, the moon excepted, have been assigned. 
Great suspicion has been thrown upon this value, how- 



PARALLAX. 61 

ever, of late years, lor various reasons; ana it is now- 
supposed that certain physical appearances that are seen 
at the transit of a planet have caused an error in the inter- 
pretation of the observations then made, so that the 
estimation is not so accurate as it was supposed to be. 
The observations in 1874 and 1882 will finally settle this 
point; but in the meantime observations have been made 
upon the planet Mars (in 1862), whereby its parallax has 
been determined similarly to that of the moon. Again, 
employing Kepler's law, we obtain a knowledge of the 
sun's parallax; and the result, 8" '94, agrees closely with 
that of the observations of 1769, interpreted as we now 
believe they should have been. The mean distance of the 
sun from this evaluation of its parallax is 91,430,230 
miles; and this is to be held provisionally as the nearest 
approach to a solution of the question, until the observa- 
tions of 1874 and 1882 have finally determined it. 

As the earth's diameter was too small a base line with 
which to measure the sun's distance without the interpo- 
sition of the planet Venus between them, so is it infinitely 
too small to aid us in obtaining a knowledge of the paral- 
lax of the fixed stars. We are therefore driven to seek a 
longer base line; and it is found in the diameter of the 
earth's orbit, the extremities of which the earth occupies 
after the lapse of half a year. Hence arises the term 
annual parallax, by which is meant the change of position 
of a star consequent upon the translation of the observer 
from one part of the earth's orbit to its opposite point, a 
distance of 183,000,000 miles. Notwithstanding this 
immense base, the annual parallax of the stars is excessively 
minute, and is hidden or masked by various other changes 
of position. Two of these, called precession and nutation, 
are caused by perturbation, and will be treated of in their 
proper place ; the third is the aberration of light. It was 
first detected by Bradley, in 1727, while endeavouring to 
solve the problem of the annual stellar parallax. The 
results of modern researches on this point will be stated 
when we come to speak generally of the stars, 



62 ASTRONOMY, 



IV. THE ABERRATION OF LIGHT. 

The discovery that light is -not propagated instantan- 
eously, but occupies a measurable time in passing from one 
point to another, was made by Roemer, a Danish astrono- 
mer, in 1675. Its velocity is very great; and though that 
of the earth in her orbit is only TUt ^ iru part as great, it is 
yet sufficiently rapid to be comparable with it. These two 
motions give rise to the phenomena of the aberration of 
light. If a hollow tube, open at either end, be carried 
along in a vertical position, and a drop of water is allowed 
to fell into it, the effect will evidently be that the water 
will strike the side of the tube. If we desire the water to 
pass through the tube while it is in motion, it is necessary 
that the tube be inclined more or less, according to the 
velocity of its motion, in the same direction as it is travel- 
ling. Though the direction in which the water falls is 
truly vertical, yet, if the eye of the observer should, in- 
sensibly to himself, be carried along with the tube, he 
would attribute to it the direction of the tube. Let us 
now apply this simple experiment to the light of a star, at 
or near the pole of the ecliptic, coming to the earth, and 
whose light therefore shines at right angles to the plane of 
the earth's orbit. The tube of the observer's telescope is 
being carried rapidly round in an ellipse along with the 
earth. It is so directed that the light of the star passes 
down it, and therefore it is inclined a little in the direction 
that the earth is travelling. It will not point to the true 
position of the star, but a little in advance towards the 
point to which the earth is tending. Yet our knowledge 
of the direction of the star is obtained from that of the 
telescope, and we are thus misled to an extent depending 
upon the relative velocities of the earth and of light. The 
star always appearing in advance of its place, in the course 
of the year it is seen to move in a minute ellipse, similar to 
that of the earth's orbit — its true place being in the centre 
of that figure. All the stars have a precisely similar 
movement; but as they are more and more removed from 



THE ABERRATION OF LIGHT. 03 

the ecliptic poles — that is, as their latitudes are less —the 
ellipses they describe are more and more compressed, conse- 
quent upon perspective or foreshortening, while on the 
ecliptic they are found to oscillate along a line on either 
side of their true place. The length of this oscillation, 
and of the major axes of the minute ellipses is the same, 
and is equal to 40" *89. Corrections have therefore to be 
applied to the observed position of all stars depending 
upon the time of the year — that is, upon the direction in 
which the earth is travelling — in order to reduce them to 
their true places, or the position in which they would be 
seen if the earth were at rest. The existence of this 
phenomenon is almost the o\i\y jihysical proof we have that 
the earth is actuallv revolving round the sun, and not the 
sun around it. 

An aberration precisely similar is produced by the rota- 
tion of the earth on its axis; but this motion is so slow, 
compared with the velocity of light, that the amount 
of the correction is very small, A little consideration 
will show that it can only affect right ascension observa- 
tions. It is known as the correction for diurnal aber- 
ration. 

Another fact is closely connected with this. The light 
of any object which reaches us must have been emitted 
from it some time earlier; and if the body is a member of 
the solar system, it will have moved sensibly in the time 
that the light was travelling to the eye. Thus the sun's 
light requires about 8 m - 17' 83 s - to reach the earth when 
at its mean distance, in which time the sun would move 
20" '445, which is also the semi-axis major of the minute 
ellipses described by the stars. The time of light passing 
to the earth from any object is generally called the aber- 
ration time; but Sir J. Herschel calls it the equation of 
light, to distinguish it from aberration properly so called. 
The correction may be made either by adding the move- 
ment of the object in the time to the observed place, or 
by supposing the observation made earlier by the amount 
of the aberration time. 



64 ASTRONOMY. 



QUESTIONS. 

1. What is meant by direct, and what by retrograde motion? 

2. What is the Ptolemaic system, and in what does it differ 
from the Copernican? 

3. How came the latter to be firmly established as the true 
theory ? 

4. State Kepler's first law. Define an ellipse, and state what 
is understood by the focus of an ellipse. 

5. Define the terms perihelion, aphelion, radius vector, line of 
apsides, eccentricity, angle of eccentricity, mean anomaly. 

6. Enunciate Kepler's law of the conservation of areas. 

7. Explain the law relating to the periodic times and the dis- 
tances of the planets. 

8. Explain the terms zodiac, ascending node. 

9. What is the first law of motion ? 

10. What balances the force of gravity acting on the moon, and 
what would happen if the earth's force was increased? 

11. State the second law of motion. 

12. State what measures the attractive force of the earth upon 
the moon. What on a stone near its surface? Compare the two. 

13. To what curves are the motions of bodies confined by the 
law of gravitation? Give examples. 

14. What is meant by perturbations ? Whence do they arise ? 

15. State the law of gravitation as enunciated by Newton. 

16. In what manner does the mass of particles composing a 
spherical body act? 

17. What is meant by the angle of the vertical and geocentric 
latitude ? 

18. Define the term parallax. 

19. Explain the method of measuring the lunar parallax. 

20. What is meant by equatorial horizontal parallax ? What is 
its mean amount in the case of the moon ? 

21. How is the distance of an object found from its equatorial 
horizontal parallax ? 

22. Why is not the sun's parallax found in the same way as the 
moon's ? 

23. Explain the method attempted by Aristarchus. What was 
the base line employed by him ? 

24. When may transits of Venus occur? Give the intervals of 
their occurrence. Why do they not happen every eight years ? 

25. Explain how the sun's parallax is determined from this 
phenomenon. 

26. State the result of the observations at the last transit of 
Venus. 

27. How have we determined the sun's distance since then? 
With what result ? 

28. What is meant by annual parallax of the fixed stars ? 



QUESTIONS. 65 

29. Explain the aberration of light, and trace its effect upon 
stars in different (celestial) latitudes. 

30. What is the maximum displacement of a star from aberra- 
tion ? 

31. What is diurnal aberration? 

32. What is meant by the time of aberration, or the equation of 
light ? 

33. What time is occupied by light coming from the sun ? How 
much will the sun have moved in the interval ? 



E 



66 



CHAPTER IV. 

I. THE SOLAR SYSTEM. 

By the term solar system is included the sun and all the 
bodies revolving round him ; planets with their attendant 
moons j comets, whether revolving in elliptical or para- 
bolic orbits, as well as meteoric streams. The primary 
planets are eight in number — Mercury, Yenus, the Earth, 
Mars, Jupiter, Saturn, Uranus, and Neptune, together 
with the group of small planets or asteroids between Mars 
and Jupiter, which at present (1872) number 125 known 
members. Planets are divided into two classes — namely, 
inferior planets, which include Mercury and Yenus, 
whose orbits are interior to that of the earth ; and superior 
planets which include all those whose orbits are exterior 
to the earth's. The inferior planets never depart from 
the sun more than a moderate distance, which is called 
their eastern and western elongations. Yenus extends 
her excursions to 47° east or west of the sun, while Mer- 
cury is confined to 29°. They never come into opposition* 
as the other planets do, but have two conjunctions, which 
are distinguished as the superior and inferior conjunctions. 
In the first case the planet is on the side of the sun removed 
from the earth, and in the latter between the earth and 
sun. To show this, suppose S to be the sun, P M C the 
orbit of an inferior planet, and E the earth. The points 
M and F are those of the inferior and superior conjunc- 
tions respectively, and P and C the positions of the planet 
at its eastern and western elongations. 

* The term opposition implies the position of a planet when dis- 
tant in longitude from the sun by 180°, or when it passes the 
meridian at midnight. A planet is in conjunction when it has the 
same longitude as the sun, or passes the meridian at the same time 
as it 



THE SOLAR SYSTEM. 



G7 



The interval of time that elapses between two successive 
similar conjunctions of an inferior planet differs consider- 
ably from its sidereal period, or the actual time taken in 
completing its orbit round the sun. If fig. 19 represents 
the orbit of Mercury, it is plain that when Mercury has 
passed round from M, through C, F, and P,the earth will 




Fig. 19. 

have moved in its orbit from E, and Mercury will not 
again come into conjunction until she arrives at some 
point between C and F, where the conjunction must take 
place — the earth having performed so much of her orbit as 
to be in the same direction at the time. This period is 
called the synodical revolution of the planet, and of course 
governs the elongations precisely as we have explained it 
to do the conjunctions. 

A further peculiarity of inferior planets is, that they 
exhibit phases similar to those of the moon. The reason 
of this is sufficiently explained in fig. 19. At inferior 
conjunction, M, the unenlightened part of the planet is 
wholly turned towards the earth; when at the greatest 
elongation, C, one-half of the enlightened part will be 
seen from the earth ; while between these points the planet 
will be gradually increasing the breadth of its crescent 
form. Between C and F a still increasing amount of the 



68 ASTRONOMY. 

enlightened part is turned towards the earth, and the 
planet will be seen to be gibbous — i.e., more than half 
moon — till at superior conjunction the whole will be seen. 
After this the form will decrease by similar degrees to the 
inferior conjunction. At the same time that it varies its 
form, it varies also its apparent size. Being most distant 
from us at superior conjunction, its diameter is then the 
smallest ; and when near the earth at inferior conjunction, 
and a very thin crescent indeed, its apparent diameter 
will be much more considerable. In this manner, the 
diameter of Mercury varies from 4^" to 13", and of Yenus 
from 10" to 66". Mars alone, of the superior planets 
presents any phase, but is never less than gibbous. 

Another classification has been proposed, namely, to 
group together the four nearest planets, which have 
numerous features in common, and the four most distant, 
which likewise have distinctive characteristics. These 
two groups would be separated from each other by the 
asteroids, which, from their minuteness and number, form 
a group of themselves. The four interior planets are all 
of moderate size, and, as we shall see, of considerable 
density, averaging about five times that of water. They 
all revolve on their axes in periods nearly the same as 
the earth (24 hours), and are unaccompanied by satellites, 
with but one exception, the earth. The four exterior 
planets, on the contrary, are bodies of very great bulk, but 
of little density, scarcely averaging that of water. They 
revolve on their axes, with much greater rapidity, in 
about 10 hours, and they all have one or more satellites. 
In some respects, therefore, this classification appears 
preferable. 

The distances of the planets from the sun has suggested 
a curious empirical law, which, until the discovery of 
Neptune, expressed those distances with some degree 
of accuracy. It was first published by Bode, and 
is known by his name. If the number 4 be taken and 
added to the products of 3, by each of the numbers of 
the series, 1, 2, 4, 8, 16, &c, the relative distances of each 
of the planets is approximately found. It will be noticed 



THE SOLAR SYSTEM. 



69 



that the distance between any two planets is generally 
double that of the preceding pair. 



BODE'S LAW. 









Empirical 


Differ- 


True 


Planet. 






Distance. 


ence. 


Distance. 


Mercury, 


4 + 3x 





4 





39 


Venus, 


4 + 3x 


1 


7 


3 


7-2 


The Earth, . 


4 + 3x 


2 


10 


3 


100 


Mars, . 


4 + 3x 


4 


16 


6 


15 2 


Ceres (Asteroid), 


4 + 3x 


8 


28 


12 


27*7 


Jupiter, 


4 + 3x 


16 


52 


24 


52*0 


Saturn, 


4 + 3x 


32 


100 


48 


95-4 


Uranus, 


4 + 3x 


64 


196 


96 


191-8 


Neptune, 


4 + 3x 


128 


388 


192 


300-6 



At the time of the publication of this law (1778), 
neither Uranus, nor Neptune, nor any asteroid had been 
discovered; and the great interval between Mars and 
Jupiter led to some speculations as to the existence of an 
unknown planet or planets to fill up the void. Uranus 
afterwards was found, and seemed to conform to Bode's 
law, and the discovery of the asteroids appeared almost to 
establish it. Nevertheless, Neptune violates it completely, 
and it can only be considered as a curious chance coin- 
cidence and as an aid to the memory. 

For a general view of the magnitudes and distances of 
the members of the solar system, we borrow an illustra- 
tion from Sir John Herschel. If upon a level field a 
globe 2 feet in diameter be placed to represent the sun, 
Mercury will be represented by a grain of mustard seed, 
on the circumference of a circle of 164 feet in diameter as 
its orbit; Venus, by a pea, on a circle of 284 feet 
diameter; the Earth also, a pea, on a circle of 430 feet 
diameter; Mars, by a large pin's head, on a circle of 654 
feet ; the Asteroids, by grains of sand, on circles varying 
-from 1,000 to 1,200 feet diameter; Jupiter, by a moderate 



70 ASTRONOMY. 

sized orange, in an orbit of nearly half a mile diameter; 
Saturn, by a small orange, its orbit being 4 of a mile 
across ; Uranus by a full-sized cherry or small plum, in 
an orbit more than 1^ miles across; and Neptune, by a 
good-sized plum, on a circle of 2| miles diameter. To this 
we will only add, to show the isolation of the solar system 
in space, that the distance of the nearest fixed star would 
on this scale be expressed by no less than 9,175 miles. 

To pursue this illustration further, and give an idea of 
the relative velocities of the planets in their orbits, we 
shall state the time that each would take to describe one 
foot of their orbits upon the same scale. For Mercury, 
4 h 3 m ; Venus, 5 h 32 m ; the Earth, 6 h 30 m ; Mars, 8 h 2 m ; 
Jupiter, 14 h 50 m ; Saturn, 20 h 5 m ; Uranus, l day 5 h 53 m ; 
and Neptune, l day ll h 39 m . 

II. THE SUN. 

We have explained in the previous chapter the method 
by which the Sun's mean distance has been determined : 
its actual dimensions, therefore, will present no difficulties. 
Its apparent diameter, as seen from the earth, varies 
slightly, in consequence of the varying distance of the 
earth from it, w^hile moving in her elliptical orbit. When, 
the latter is at perihelion, upon January 1, it measures 
32' 36"-2; when in aphelion, upon July 3, 31' 32"-0 in 
diameter; at the mean distance, 32' 3"*6. Now, to present 
so large an angle as this at the distance of 91,430,23(3 miles, 
a globe would require to be 852,680 miles in diameter, — a 
magnitude that at once places the sun as worthy of being 
the centre of a system of planets such as ours. If the 
earth was placed in the centre of a hollow globe of this 
size, the moon could perform her revolution within it, and 
a margin of nearly 200,000 miles would yet be left beyond 
her at every point of her orbit. 

When we come to compute its bulk, we find it to 
exceed that of the earth, as 1,249,500 to 1, or that ro 
is equal in size to 1^ million of earths. But we have 
further to inquire, what is the density of the sun : is the 



THE SUN. 71 

specific gravity of the materials of which it is composed as 
heavy or heavier than those of the earth? This is not, as 
it would seem, a very difficult problem. "We must com- 
pare the effect of the gravity of the earth upon the moon 
with that of the sun upon the earth. The effect of the 
earth's gravitation upon the moon in a given time is 
measured by the line C m (see fig. 14), the deviation of 
the moon from the direction of the tangent to her orbit; 
and, knowing the dimensions of that orbit, we can com- 
pute the length of C m in feet.* To find what would be 
the effect, supposing the moon was at the same distance 
as the sun, is the next step. Gravity decreasing as the 
square of the distance increases, it follows that since the 
sun is 383 times more distant from us than the moon, the 
effect of gravity would be diminished to -3I3-2 or ytwIttw 
part. From the dimensions of the earth's orbit we must 
next obtain the distance through which the sun pulls the 
earth in the same time — that is, its deviation from the 
direction of the tangent, and, comparing the two, we have 
the ratio of the attractive forces of the sun and earth. 
When these calculations are made, it is found that the 
sun's attractive power — that is, its mass or weight — is 
315,115 times that of the earth; but its bulk being, as 
before stated, 1,249,500 times the earth's, it follows that 
the specific gravity of the matter composing it can only be 
\ as heavy as that composing our own globe. This frac- 
tion, therefore, represents its density, that of the earth 
being considered as unity. It has been conjectured, from 
the comparative lightness of the materials of the sun, that 

* If we suppose the orbit to he a circle, and no appreciable 
error will arise from this supposition, this is very simple. C m 
being equal to M G-, we have only to solve the triangle m G- E to 
obtain this. The augle m G E is a right angle ; GEm is known, 
being the mean orbital motion in the time taken, as an hour or a 
day; and E m is the radius of the mqon's orbit, also known. M G 
may thus be found, and its difference from M E is the quantity 
required. The reader will bear in mind, that if three parts of a 
plane triangle are known, provided they are other than the three 
angles, any other parts of it may be found by the simplest appli- 
cation of trigonometry. The effect of the sun's attraction on the 
earth will be found in a precisely similar manner. 



72 ASTRONOMY. 

its centre is maintained at an intense heat, and that thus 
the pressure of its particles towards the centre, which 
would cause a great density, is overcome. We shall soon 
see from various experiments, that the average density of 
the materials of the earth is about 5*67 times that of 
water ; from which it follows, that that of the sun is about 
1*43 times the density of water. From this data it would 
be easy to compute the actual weight of the sun in tons, 
but the number expressing it extends to twenty-eight 
figures, and is perfectly incapable of giving any idea to the 
mind. 

We can go yet another step. The gravity of a sphere, 
acting always as though its particles were collected at the 
centre, objects upon the surface of the sun, are removed 
from the centre of attraction by the length of its radius, 
or 426,340 miles; and its gravity being 315,115 times that 
of the earth, we can compare the weight of bodies upon 
the surfaces of the earth and sun. It will be found on 
making the calculation, in accordance with the law of 
gravitation, that a body weighing only 1 pound at the 
earth's surface would weigh at the surface of the sun 
2 7 J- pounds. A man weighing 12 stones on the earth, 
if carried to the sun, would weigh more than 2 tons : 
muscular energy would be greatly overpowered, and he 
would be crushed by his own weight. 

The most careful observations have failed to detect anv 
ellipticity in the figure of the sun, and we must therefore 
assume it to be a perfect sphere. That it revolves upon 
its axis in 25 days 7 h 48 m , and that its equator is in- 
clined to the ecliptic by about 7° 20' is determined by the 
observation of the spots on its surface, which, from their 
importance, deserve a somewhat detailed description. 

With the ancients, and during the middle ages, the 
purity of the sun was held almost as an article of faith, 
notwithstanding that spots large enough to be visible to 
the naked eye had occasionally been seen upon it. It was 
one of the first triumphs of the telescope, in the hands of 
Galileo and others, to reveal the fact that the sun was 
rarely without a greater or less number of such blemishes. 



THE SUN. 



73 



The general appearance of the spots is an intensely dark 
central space of tolerably regular form, surrounded by a 
more irregular belt of semi-luminous matter. The interior 
space is termed the nucleus of the spot, and the exterior 
the penumbra. The forms assumed and the general 
appearances are very various: sometimes nuclei are seen 
without any accompanying penumbrae, and more often 
penumbrse without any accompanying nucleus, while very 
frequently one penumbra will embrace several nuclei. 
Not unfrequently a large spot will be crossed by a bright 
patch, presenting the appearance of a luminous bridge — a 
name which is sometimes applied to it (see fig. 20). Spots 




Fig. 20. Solar Spots. 

are often of great extent, and appear to have a tendency to 
group themselves together; neighbouring groups have been 
observed likewise to tend away from each other. Chains 
of spots of various size and form are often seen extending 
100,000 miles or upwards from end to end, generally 
parallel to the sun's equator; and one or two members of 
such a group will occasionally measure 10,000 miles 
across. Sometimes single spots much larger than this are 
seen, and many are on record varying from 30,000 to 
45,000 miles in diameter. These may generally be seen 
with the naked eye, if the sun be obscured by haze or fog. 
Careful photometric observations made by Sir W. Herschel 
shew that the penumbra emits scarcely half the light 
which is given by the pure surface of the sun, while the 
nucleus he considered to emit only 7-thousandths as much 



74 ASTilONOMY. 

light as the bright parts: its intense blackness is therefore 
to a considerable extent produced by contrast. 

Another remarkable peculiarity is the frequent change 
of form, the sudden bursting out and as rapid disappear- 
ance of the spots. Their duration is very various; many 
last only a few days and some only a few hours, and per- 
haps the majority do not exist long enough to be brought 
a second time into view by the sun's rotation; while cases 
are on record of spots disappearing suddenly under the 
eye of the observer. On the contrary, others remain so 
long as to be visible during several revolutions of the sun. 
Schwabe has followed a group for sixteen months; and 
many observers speak to their existence for periods varying 
from three to six months. It will be understood that, 
though not absolutely fixed to the sun's surface, they are 
yet attached to it, and are not of the nature of floating 
clouds. 

The physical cause of the solar spots has long been a 
subject of speculation. That they are depressions in the 
surface of the sun is certain, since, when approaching the 
margin or limb of the sun, it is always observed that the 
penumbra on the side nearest the margin is broad and 
well seen, while that upon the other side becomes narrower 
and narrower, until it disappears entirely from the effect 
of perspective. Upon one or two occasions, when a large 
spot has been upon the margin, a notch has been observed 
in the limb of the sun. That the nucleus is the opaque 
body of the sun itself is also generally held, while above 
this two atmospheres are supposed to exist. The upper 
one, self-luminous, and called the photosphere, is that 
from which we derive light and heat; the interior one is 
non-luminous, but capable of reflecting the light of the 
superposed cloudy atmosphere. The disruption of both 
atmospheres is supposed to be caused by the upheaval of a 
body of highly heated elastic gas produced below them, 
or by the down-rush of cooled gas from above — both 
theories having their supporters. Upon no other hypothesis 
can the sharply-marked upper and lower outlines of the 
penumbra be explained. 



THE SUN. 75 

To find the period of the sun's rotation and the inclina- 
tion of his axis to the ecliptic is by no means an easy- 
problem. The changing forms and want of perfect fixity 
in the spots is a great source of error in the results. A 
well defined spot which promises to be permanent for a 
few revolutions must be selected, and its position on the 
solar disc must be carefully measured from day to day. 
It will ordinarily be found to pursue a curved path, in 
consequence of one or other pole of the sun being turned 
a little towards us, and it is more rapidly performed near 
the centre of the disc, owing to the convexity of the surface. 
Upon two days of the year the earth will pass through 
the plane of the sun's equator, and the paths of the spots 
across the sun will then appear to be in straight lines. 
Midway between these dates the curvature will be greatest, 
the pole of the sun being duly turned towards the earth, 
the position most favourable for these observations. The 
amount of the curvature at this time affords the means of 
finding how much towards us the pole is tilted. From 
numerous observations of this kind, the inclination of the 
sun's equator to the ecliptic has been found to be about 
7° 20' ; but, for the reasons stated, the amount is doubtful 
to perhaps ^ a degree. Similar observations made upon 
a spot which shall have existed during several revolutions 
will give with more accuracy the period of his rotation, 
which has been found to be about 25 days 8 h ; but this 
may be in error as much as \ hour, from the same cause. 
It is not this period, however, that governs the reappear- 
ance of the spots; for it must be remembered that the 
earth is revolving round the sun in the same direction as 
his rotation, and that the spot will not arrive at the same 
position on the apparent disc till the lapse of 27 days 7 h . 
This is quite analogous to the synodical revolution of a 
planet. The length of time that a spot is visible is there- 
fore nearly fourteen days. 

In the neighbourhood of the spots, or near where one 
has disappeared or may be expected to appear shortly, are 
generally seen long branching streaks of light, fully as 
intense as the brightest parts of the sun, and when near 



i b ASTRONOMY. 

the margin these are very conspicuous. That they are 
closely connected with the spots is certain, and they are 
believed to be elevations or heaped-up ridges of the photo- 
sphere, produced by the same convulsions as the spots are. 
They are termed Faculae. The whole surface of the sun, 
when carefully examined, is found to present a generally 
mottled appearance, not unlike the lighter parts of a mezzo- 
tint engraving. "Very great attention has been paid to 
this lately; and with high magnifying powers it has been 
found to be produced by the dark interstices between the 
luminous masses of the outer atmosphere, which from 
their form have been called willow leaves, rice grains, &c. 
These overlie each other in every conceivable direction, 
but not as thickly but that they leave small interstices of 
considerable blackness, from the grouping of which the 
mottled appearance of the sun arises. Curiously enough, 
this is more noticeable within the region where spots are 
usually found, and hence cannot be entirely unconnected 
with them. 

Certain zones of the sun's surface are remarkable for 
the magnitude and frequency of spots. They are rarely 
seen, for instance, on the solar equator, nor yet at a distance 
very remote from it. The northern hemisphere is more 
prolific of spots than the southern, and from about 8° to 
to 28° of solar latitude, both north and south, are the 
regions of especial fecundity. Spots are occasionally seen 
beyond these limits, but the polar regions of the sun are 
always quite free from them. 

That the solar activity produces an effect on terrestrial 
phenomena is most clearly shown by an observation 
which was made by two observers in 1859. A bright 
mass of the photosphere was seen projected over the black 
nucleus of a spot, and, after moving with extreme 
rapidity, disappeared. Simultaneously there was a great 
disturbance in the direction of the magnetic needle, 
and a magnetic storm of great violence prevailed for 
some time afterwards, accompanied by a vivid display of 
aurora borealis. That a connection exists between all 
these phenomena is fully admitted, but of what nature the 
bond of union may be, is not at present known. 



THE SUN 77 

The last fact that we shall have to mention in connec- 
tion with this subject is the recent discovery, that there 
exists a definite periodicity in the frequency of the spots. 
Schwabe, whose long-continued observations are invaluable 
on this point, has succeeded in showing that in periods of 
rather more than eleven years there occurs a maximum 
and a minimum frequency of spots, and that this period of 
solar activity, though not before recognized, is confirmed 
by the observations of more than two centuries. A pre- 
cisely similar period is known to exist in the variation of 
the magnetic declination, of which the maxima and minima 
agree precisely with those of the spots. There are exactly 
nine such periods in each century; and the first year of 
each being one of minimum frequency, it is easy to calcu- 
late the degree of activity to be expected in any year. 
Carrington, who has also paid much attention to the sun's 
spots, says, that as the time of minimum frequency 
approaches, the spots seem to have a tendency to occur 
near the equator, and gradually die out there. Afterwards 
they are seen to commence again, remote from the equator, 
and slowly progress towards it as a second minimum draws 
near. Attempts not altogether successful have been made 
to show that there is a similar period to be observed in 
meteorological phenomena, years of great solar activity 
being warmer, drier, and more fruitful than others. 
Supposing such to exist, it is certain that it is not very 
prominently marked. 

For further information relative to the physical con- 
stitution of the sun, we have to examine the phenomena 
which are witnessed during the totality of a solar eclipse. 
The theory of eclipses will be discussed in the following 
chapter; at present it is only necessary to know that at 
times the opaque body of the moon places itself between 
the earth and sun, and that acting as a screen to hide the 
overpowering light of the photosphere, we are able to 
examine some of the fainter details, which are quite 
invisible at other times. That the sun possesses an 
exterior gaseous envelope of great extent, more nearly 
approaching our ideas of an atmosphere, is rendered 



78 ASTRONOMY. 

probable by an appearance readily noticed. The amount 
of light received from the borders of the solar disc is 
palpably less than from the central parts, giving in the 
telescope unmistakable indication of convexity; and the 
most natural way of accounting for this, is, that the light 
from the borders, in consequence of its obliquity, has to 
pass through a dense stratum of atmosphere, sufficiently 
transparent to allow the greater part of it to pass, but 
yet, like our own, capable of absorbing a part also. The 
observations of the eclipsed sun have rendered this a 
certainty. 

The principal features observable on these occasions 
are portrayed in the frontispiece. The surrounding 
corona or " glory " that bursts forth with startling sudden- 
ness the moment that the last remnant of the photosphere 
is hidden by the dark moon, must be regarded as a 
reflection of the sun's light by his atmosphere. The 
latest observations point to a division of this corona into 
two parts, a narrow belt, near the sun, faintly self- 
luminous as well as reflective, and an exterior and broader 
part, gradually fading away in intensity, reflective only. 
Below these, and abutting upon the photosphere, is the 
region known as the chromosphere, occupied by a greatly 
heated gas of extreme tenuity surrounding the sun com- 
pletely, but, being subject to the disturbances of the 
photosphere, is here and there thrown together in 
enormous masses, in the form of red flames or promi- 
nences. These are continually undergoing changes of form, 
and move with great rapidity. A height of 100,000 
miles above the photosphere is often reached by them. 
We have some evidence, revealed by the newly founded 
science of spectrum analysis, of yet another layer of gas so 
highly heated that metals such as iron continue there in 
a state of vapour. 

There are thus no less than six successive strata of 
atmospheres covering the solid body of the sun : — 1st. The 
dense non-luminous but strongly reflecting cloudy atmo- 
sphere of the penumbra. 2nd. The highly luminous 
photosphere. 3rd. The highly heated region of luminous 



THE SUN. 79 

metallic gases, itli. The more light and mobile chromo- 
sphere. 5th. The self-luminous and reflective corona; 
and, 6th. The non-luminous outer corona or halo. The 
last two are believed to be something of the nature of a 
perpetual solar aurora, the hypothesis that their luminosity 
is produced by electric currents being very probable. 

We shall conclude this notice of the sun by attempting 
to give some idea of the amount of light and heat given 
forth by it. The earth, as seen from the sun, being only 
a minute disc of 18" diameter, and the intensity of heat 
diminishing as the square of the distance increases, it 
follows that a most insignificant fraction of the solar heat 
reaches the earth. It has been calculated that the 
annual expenditure of heat by the sun is 2,381,000,000 
times that received by us, and it has further been found 
that the amount we receive in a year would be sufficient 
to melt a layer of ice thirty-eight yards thick, and covering 
the whole globe. Photometric observations made upon the 
light of the sun have proved it to be 618,000 times that 
of the full moon, and equal to 5,563 wax candles at a 
distance of one foot from the eye. From whence arises 
the energy which maintains this continual drain of heat 
and light is a problem upon which even speculation fails, 
and the question must remain to be solved in the future; 
but it has been conjectured that meteoric streams pouring 
into the sun may supply the waste of combustion. There is 
one phenomena which gives some colour of probability to 
this theory. Accompanying the sun is a hazy nebulous 
cone of light — an indication of the existence of a mass of 
material particles, in the form of a very flat spheroid or 
lens, extending as far as the earth, or perhaps beyond it. 
This is often seen in tropical climates, and sometimes in this 
country, after sunset in early spring and before sunrise in 
autumn. It is called the zodiacal light, and resembles the 
milky way in appearance. It always occupies a position 
near the ecliptic, within the zone of the zodiac; hence the 
name. By some it is supposed that it is composed of 
meteors revolving round the sun in spiral orbits, and con- 
tinually falling into it. It stretches to a distance of 50° 



80 ASTRONOMY. 

or 60° from the sun, and hence must be of immense 
extent. No satisfactory explanation has been given of 
the phenomena, but for the present, it may be considered 
as most likely to consist of meteoric matter, either 
supplying the loss of the solar combustion, or simply 
revolving round or with the sun. On the meteoric 
hypothesis it has been calculated that, to sustain the 
sun's enormous expenditure of light and heat, a depth 
of 24 feet per annum of such matter must be deposited 
all over its surface, which would increase its apparent 
size 1" in 100,000 years. However, this is far from 
being generally accepted as a satisfactory solution of 
this difficult question 



III. MERCURY. 

This planet, in spite of its constant proximity to the 
sun, was known to the ancients. It revolves round 
that body in a shorter period than any other planet, 
and is, of course, the nearest to it. The length of its 
synodical period, or that in which it will pass through 
all its phases, from one inferior conjunction to another, 
is 115 days 21 h ; # but its actual time of revolution 
round the sun, or sidereal period, is only 87 days 23 h 
15 m 43 -91 s . This latter is determined by observing 
the interval of time between the successive arrivals 
of the planet at its node or the point of crossing the 
ecliptic. The node being a fixed point in its orbit, or 
only subject to very slight displacement, it serves well 
to find the sidereal period; and, notwithstanding the 
intricate movements of the planets, their intervals of 
departure from and arrival at the ecliptic are in- 
variably equal. Of all the larger planets, Mercury 
has the most elliptical orbit, being more than 14,000,000 
of miles more distant from the sun at aphelion 

* During 23 days the planet has a retrograde motion; in the 
remainder it will have direct motion. 



MERCURY. 81 

than at perihelion, though its mean distance is only 
35,392,470 miles. The eccentricity may be expressed 
by the fraction -£>-^q- Its orbit is also more inclined 
to the ecliptic than are those of the other large planets, 
and its last peculiarity is, that it is the smallest 
planet, with the exception of the asteriods, and the 
most dense. 

In consequence of its apparent and also of its real 
nearness to the sun, very little is known of its physical 
constitution. Its lustre is most brilliant, and effectually 
hides its features; but it is believed to possess a dense 
cloudy atmosphere, which may possibly protect it from 
the extreme heat of the sun, which will shine there with 
seven times the intensity that it does upon the earth. 
Mountains have been seen upon it of very great height, 
certainly exceeding 10 miles, or about -^-g- part of its 
diameter. This is relatively about six times higher than 
the highest summits upon the earth, the tallest peak of 
the Himalaya being only Tt -^-^ part of £the earth's 
diameter. From the observation of one of these moun- 
tains, the time of its rotation on its axis has been found 
to be '24 h 5 m 30 s ; but the difficulties incident to 
such observations may render the result rather doubtful. 
Its form has been also examined by several observers, 
but only one has been able to detect satisfactorily its 
ellipticity. It is fixed at ^-; and the equatorial diame- 
ter being estimated at 2,961 miles, the polar will be 
about 100 miles less. 

To discover the mass of Mercury has been a very 
difficult problem, and it is still to some extent a matter 
of doubt. Having no satellite, we are only enabled 
to find its weight or attracting power by observing 
the slight deviations in the motions of bodies that may 
pass near it. A small periodical comet has twice passed 
near it, and from the distance it has been pulled from 
its true orbit, an estimation of the mass has been made. 
It is not surprising that in consequence of the minuteness 
of these inequalities that different values have been 
obtained by different calculators. The most probable 
a. p 



82 ASTRONOMY. 

amount is x.sTs.TTr P ai ^ °^ tne sun ' s niass; and while its 
insignificance makes it so difficult to obtain, it at the 
same time renders the knowledge of the amount of little 
importance, since the effect it can produce upon the other 
bodies of the system must be proportionally slight. From 
this value of the mass the density of the planet will be 
found to be about 7*27 times that of water. 

Like Venus, Mercury occasionally transits the sun's 
disc, but more often than it. The transits occur at 
intervals of either seven or thirteen years, and always 
take place in either May or November, according as the 
planet is at the descending or ascending node. The 
reason why the transits are confined to these months is, 
that the sun upon the 6th May and 8th November passes 
over the degrees of longitude in which the nodes are 
situated ; and it is only when the planet is near these 
points that a transit can take place. Transits of Venus 
are similarly obliged to take place early in the months of 
June or December. 

The transits of both planets were first predicted by 
Kepler; but those of Mercury are by no means so valuable 
to the astronomer as those of Venus, as may be seen from 
the consideration of fig. 18. The sun's parallax is quin- 
tupled by the interposition of Venus ; but the ratio of the 
distances of Mercury from the earth and sun being as 61 
to 39, the solar parallax is only multiplied by |- by the 
interposition of that planet, which is still too small an 
angle to measure satisfactorily. 

Peculiar phenomena are seen to take place when a 
planet is upon the sun's disc, for which, until lately, no 
satisfactory reason was assigned. It is a principle of 
optics that when a dark object is seen upon a bright 
white background, the white light encroaches a little upon 
the black; and hence a planet in this situation is seen to 
be rather smaller than it really is. Also, if a bright 
object is seen upon a dark background, it dilates itself, 
and thus the sun appears rather larger than it really is. 
This is called the irradiation of light. The sun's apparent 
size is still further slightly augmented from another cause, 



VENUS. 



83 



A, 






depending upon the action of light in passing through the 

telescope, which is known as diffraction. 

Now, when the diminished disc of the planet \ 

touches the interior of the augmented disc 

of the sun, both these optical effects are 

at once destroyed, — the planet is elongated 

at the point of contact, and the sun's disc 

seems to retreat to meet it. In this way 

the planet assumes a somewhat pear-shaped 

form. In tig. 21 the real borders of the 

sun and planet are marked by dotted lines, 

and the apparent borders by bold outlines. 

When the former come to touch, as at B, 

there being no longer any real source of 

light between the apparent borders, a dark 

belt is formed, and the planet assumes the 

form C. This occurs at both the ingress 

and the egress of the planet, and gives rise 

to an error, which, in the case of the planet 

Venus, has entailed a wrong evaluation of 

the solar parallax. Fig. 21. 




IV. VENUS. 



Venus is the next planet in order from the sun, and 
revolves round him in a very slightly elliptical orbit, 
the eccentricity being only yx^Vtt* ^ s mean distance 
from the sun is 66,134,380 miles, and the difference 
between the greatest and least distances does not 
amount to 1,000,000 miles. It performs its revolution 
in 224 days 16 h 49 m 8 s , but for its synodical period 
requires 583 days 4 h 48 m ,* which is the interval between 
the successive appearances of the planet in the same 
position as a morning or evening star — i.e., at its western 
and eastern elongations. : Its diameter measures 7,511 
miles, or but little less than that of the earth ; and 

* Venus retrogrades during 42 days of her synodical period. 
Being an inferior planet, this occurs on either side of her inferior 
cod junction. 



84 ASTRONOMY. 

no polar compression has been observed. This arises not 
so much from its possessing a perfectly spherical form, 
although its ellipticity cannot be great, but from the rarity 
of a conjunction favourable for the purpose of determin- 
ing it, namely, during a transit across the solar disc. 

Having no satellite, the mass of Venus is almost as 
difficult to determine as that of Mercury; but being near 
the earth, and of nearly the same magnitude as it, the 
effect of its gravitation is felt in displacing the earth from 
her true orbit. The most satisfactory accordance exists 
between the various calculators, and the mass is set down 
with considerable exactness, at -g-g-oiWrr part of the sun's 
mass. Calculating, as in the case of the earth or sun, the 
bulk of the planet, and comparing it with the mass, we 
find the density of Venus to be 5*36 times that of water, 
and very nearly equal to that of the earth — the planet 
which in very many respects it seems to resemble closely. 

Of all the planets, Venus shines with the greatest 
brilliancy, being often visible in daylight, at noon, and 
less frequently, when favourably situated it will cast a 
very perceptible shadow at night* This does not happen, 
as might be supposed, when the whole disc is illuminated, 
for at that time Venus is very remote from us, but when 
it is a crescent, less than half-moon between the greatest 
elongation and inferior conjunction. Its diameter is then 
considerable; but as it approaches inferior conjunction, 
the diminution of the breadth of the crescent more than 
compensates for its lessening distance, and it declines in 
brilliancy. Its lustre, like that of Mercury, veils the 
peculiarities of surface, &c; but from certain spots on its 
disc its time of rotation has been accurately deter- 
mined—namely, 23 h 21 m 23 s — and the axis of that 
rotation has further been found to be inclined to the 
ecliptic about 75°. That it possesses an atmosphere of 
considerable density is certain; and from the amount of 
twilight which has been observed upon the unilluminated 
portion of the planet, the amount of horizontal refraction 

* The author has witnessed both these proofs of brilliancy — the 
first notably in April, 1870; the second in November, 1863. 



QUESTIONS. 85 

(hence the density of the atmosphere) has been found 
almost precisely equal to that upon the earth. Mountains 
have likewise been seeu upon this planet of very great 
height, and the highest summits have been estimated at 
o-|q- of its diameter ; but it is necessary to state that, owing 
to the delicacy of all such measurements, no great accuracy 
is attainable. 

QUESTIONS. 

1 . What is meant by the solar system ? 

2. State the distinction between superior and inferior planets. 

3. Explain the terms conjunction, opposition, and elongation. 
What is the extent of the greatest elongations of the two inferior 
planets ? 

4. Explain the terms superior and inferior as applied to con- 
junctions ? 

5. What is meant by the synodical period of a planet ? Why 
does it differ from the sidereal period ? 

6. Trace the phases of an inferior planet throughout its synodical 
revolution. At what phase will the apparent diameter be 
greatest ? 

7. State the principal peculiarities that the four interior planets 
have in common, and also the four exterior. 

8. State Bode's (so-called) Law. In what case does it fail ? 

9. Give the illustration mentioned in the text of the relative 
sizes and distances of the planets ? 

11. Why does the apparent diameter of the sun vary? Give its 
limits, and also the real diameter in miles ? 

12. Compare the bulk of the sun with that of the earth. 

13. How is the mass or weight of the sun measured against that 
of the earth ? How much does the former exceed the latter ? 

14. What is the average specific gravity of the materials of the 
sun compared with those of the earth, also compared with water? 

15. How are the effects of gravity at the surfaces of the earth 
and sun compared, and with what result ? 

16. Describe the usual appearance of a sun-spot, and explain 
the terms nucleus and penumbra, as applied to these phenomena. 

17. What amount of light is emitted from the several parts of a 
solar spot ? 

18. Give some idea of the duration, magnitude, and mode of 
grouping of the spots. 

19. State the generally received explanation of the origin of the 
spots. What is meant by the photosphere ? 

20. How is the inclination of the sun's axis to the ecliptic 
found ? Give the amount of that inclination. 



86 ASTRONOMY. 

21. How is the time of rotation found ? Give it, and likewise 
the period which determines the return of a spot. 

22. What are facula3, and from what arises the mottling of the 
sun's surface? 

23. Where are spots most frequent, and what parts are alwa3 r s 
free from them ? 

24. With what terrestrial pheuomena are the spots connected ? 

25. What period is recognized as governing the frequency of the 
spots? Does the same period occur in any other pheuomena? 
What effect has the period upon the position of the spots ? 

26. Give the reason for the diminution of light towards the 
margin of the solar disc. 

27. What is the corona, and from whence does its light come ? 

28. What is meant by the chromosphere, and what gives rise to 
the red flames or prominences ? 

29. Describe the several atmospheric envelopes of the sun in 
order from its surface. 

30. What is the diameter of the earth as seen from the sun, and 
what proportion of its light and heat actually reaches us ? 

31. Compare the light of the sun with that of the full moon. 

32. Explain the meteoric hypothesis of the maintenance of the 
solar light and heat. 

33. What is the zodiacal light— give some explanation of it. 

34. Give the duration of the sidereal and synodical periods of 
Mercury, and how is the former most readily determined ? 

35. Give the mean distance of Mercury from the sun, and state 
some peculiarity regardiug the ecceutricity of its orbit. 

36. What is the principal obstacle to the making observations 
on the surface of Mercury ? State what is known of its physical 
constitution. 

37. Give its time of rotation, and state from what it has been 
determined; also its real diameter, and the amount of polar 
compression. 

38. How has the mass of Mercury been obtained ? Give it, and 
likewise its density. 

39. At what intervals and in what months do transits of Mer- 
cury take place ? In what months transits of Venus ? 

40. Why are transits of Mercury of little astronomical impor- 
tance ? 

41. Explain what is meant by irradiation, and state its effects 
upon the sun and a planet transiting. 

42. To what phenomena does it give rise at the ingress or egress 
of a planet ? 

43. Give the mean distance of Venus, and some idea of the 
eccentricity of its orbit. 

44. Give its synodical and sidereal periods, and its true diame- 
ter in miles. 

45. Why is the polar compression of Venus at present unknown? 



QUESTIONS. 87 

46. How is the mass of Venus found, and what is the result ? 
Give also the density compared with water. 

47. At what points of her synodical revolution is Venus at its 
greatest brilliancy ? 

48. Give its time of rotation, and state what peculiarities of 
surface has been noticed upon it. 

49. How do we know that it is surrounded by an atmosphere? 
Summarize the points of similarity between the earth and Venus. 



88 



CHAPTER V. 

I. THE EARTH. 

The globe we inhabit is the next planet in order from 
the sun; and being also that one of which it is possible to 
learn the most, it is necessarily taken as the standard 
with which to compare all the others. The mean distance 
of it from the sun is used, as the astronomical unit of 
length, and as this can only be found after a thorough 
examination of the size and form of the earth, these have 
already been discussed. The time of its rotation on its 
axis and that of its revolution round the sun form the 
standards for the measurement of duration; and finally, 
its mass affords the means of determining that of the sun, 
as well as indirectly the masses of the planets also. There 
remain, however, a few points to which it is necessary to 
allude. The orbit which it describes round the sun at a 
mean distance of 91,430,230 miles is very little eccentric, 
though more so than that of Yen us, being -5-9^-g-. When at 
perihelion upon January 1, it is rather more than 3,000,000 
miles nearer the sun than at aphelion on July 3. As this is 
opposed, at least for the northern hemisphere, to what 
might be expected from the greater heat of summer, it is 
necessary to explain to what causes the warmth of the 
seasons is to be ascribed. 

When a rotatory motion is given to a globe, there is, 
owing to the generation of a centrifugal tendency, scarcely 
anything in nature more permanent in direction than the 
axis of that rotation. In obedience to this feature of 
motion, the axis of the earth, during every part of its revo- 
lution round the sun, is carried parallel to itself. The 
effect of this will be most readily appreciated by a reference 
to the diagram (fig. 22). The axis of rotation being 



THE EARTH. 



89 



inclined at an angle of 66° 32' to the plane of the orbit — 
i.e, to the ecliptic — is represented by the line P p, and the 




Fig. 22. 

equator by E Q, at four several positions of the earth. At 
A, representing the position at the vernal equinox, the 
whole hemisphere from pole to pole is illuminated by the 
sun, S, and during the rotation every part of the earth 
will have an equal share of light and darkness. Similarly, 
at the autumnal equinox, C, the enlightened hemisphere, 
though turned away from the spectator, will extend from 
pole to pole. At B, the summer solstice for the northern 
hemisphere, the north pole is turned towards the sun, and 
within a circle of 23° 28' radius the sun will not set. 
On the contrary, within an equal circle, of which the south 
pole is the centre, night will continue throughout the 
twenty-four hours. Further, the sun will be vertical over 
a point 23° 28' north of the equator, or the tropic of 
Cancer. At the northern winter solstice, D, the south 
pole will be turned towards the sun, which will be verti- 
cal over the tropic of Capricorn, and the position of the 
hemispheres, with reference to the sun, will be exactly 
reversed. Hence arise the principal divisions of the globe 
into zones — the two tropics and the arctic and antarctic 
circles being the boundary lines. 

From the consideration of fig. 23, which is the position 



90 



ASTRONOMY. 



of the earth at the northern summer solstice, we shall be 
able to trace the effect of this upon temperature. M S, 



"jsr P 




N" p 



Fix. 23. 



lig. 24. 



T S', &c, being the direction of the solar rays, the vertical 
circle, L M N, will separate the enlightened and dark 
hemispheres of the earth. If, then, we take any point, T, 
it will be seen that the nearer this is to the arctic circle, 
M A, the longer will be the day, represented by a broad 
outline, T L, and the less the night, represented by a fine 
outline, L D. The exact reverse of this is shown in figure 
24, which represents the position of the earth at the 
northern winter solstice. It will further be seen, by 
comparing figs. 23 and 24, that the direction of the 
solar ray, T S', is much more oblique to the surface at T, at 
the winter, than at the summer solstice. Now, so long as 
the sun is above the horizon of a place, the earth is 
receiving heat from it; but when it has set, the earth 
parts with what she has received, radiating it back again 
into space. It will appear, therefore, that at the summer 
solstice the northern hemisphere will receive more heat 
in the long day than it can part with in the short night, 
and hence is accumulating a supply that makes each suc- 
ceeding day warmer (disregarding local causes), until the 
days becoming shorter, the daily supply diminishes. This 
is the reason why the warmest part of the summer is not 
at the solstice, but nearly a month later. Again, if we 
suppose a bundle of rays to fall perpendicularly on the 



THE EARTH. 91 

earth, they will all be absorbed within a comparatively 
small area; but if a similar bundle fall in an inclined 
direction, they will cover a much larger space, or the same 
amount of heat is more distributed. Thus the more 
oblique direction of the sun's rays, as well as the shorter 
time that it is above the horizon, contribute to make the 
winter cold, in spite of our greater nearness to the sun, 
while the greater length of the day, and the less inclina- 
tion of the solar rays, both tend to produce the heat of 
summer. 

It must not be imagined, however, that our proximity 
to the sun during the northern winter has no sensible 
effect in ameliorating that season, as also of increasing the 
heat of the southern summer, with which it is coincident; 
but it requires to be borne in mind that when near peri- 
helion the earth is moving with its greatest speed; and 
hence the greater heat of the southern summer is exactly 
compensated by its shorter duration, and the amount of 
heat received by either hemisphere is thus equalized. 

It w T ill be necessary to make a few remarks upon the 
problem of determining the position of places on the 
earth, or their geographical latitude and longitude. The 
first is very easily found, as it is always equal to the alti- 
tude of the celestial pole above the horizon; and since we 
have a most brilliant pole star, in the northern hemisphere 
at least, we have only to measure its altitude with the 
mural circle or altazimuth, if the station be on land, or 
by the sextant, if at sea, and making certain corrections 
for refraction, its non-coincidence with the pole, or its dis- 
tance from the meridian at the moment of observation, and 
the latitude is found. There are various other methods in 
use, but all more or less resemble this, and are invariably 
very simple in principle. 

The great problem of finding the difference of longitude 
is a more difficult question; but still, if the stations are on 
land, and within a moderate distance of each other, it is 
not troublesome. We have stated that the difference of 
longitude is nothing more than the difference of local 
time at the two places. If, then, we have two observa- 



92 ASTRONOMY. 

tories, furnished with clocks and transit instruments, by 
which the former can be made to indicate true local time, 
we have only to find some means of comparing the two 
clocks to know the difference of longitude. The most 
obvious method is to carry a chronometer, or a number of 
chronometers, to avoid error, from the one to the other, by 
which the difference of the two indications will be at once 
found. If not too remote, a better plan is to observe 
simultaneously at either station a concerted signal, as the 
firing of a rocket, which event will be referred to different 
local times at the two stations, and hence the difference of 
longitude will be found. The sudden appearances of 
meteors or shooting stars have been successfully employed 
as instantaneous signals visible over a great extent of 
country. More recently, the electric telegraph has been 
used to compare the clocks at the two stations, and 
undoubtedly affords the best means of doing so; but the 
details of the application of this method are beyond the 
limits of the present work. 

It is manifest, however, that none of these methods will 
serve to determine the longitude at sea, where the sextant 
is the only instrument that can be used, and we are forced 
to have recourse to purely astronomical processes. Of all 
the heavenly bodies, the moon is by far the most rapid in 
its movements; and though these are extremely complica- 
ted, they have now been thoroughly mastered by the 
theory of gravitation. It has thus become possible to pre- 
dict and publish beforehand its place with reference to 
certain standard stars with very great accuracy for very 
short intervals (three hours) of Greenwich local time. 
The position of the moon among the stars — that is, its dis- 
tance from one of the standards — is to be measured by the 
sextant, and compared with the distances at fixed hours of 
Greenwich time in the published tables, when, from the 
rate of the moon's motion at the moment, the Greenwich 
local time of the observation will be found, and the devia- 
tion of the chronometer time therefrom, or its error. It 
remains to ascertain the local time, which may be found 
in various ways, as, for example, by observing the chrono- 



DENSITY OF THE EARTH. 93 

meter times at which the sun is at equal altitudes on either 
side of the meridian. The mean of these is the Green- 
wich time of the local apparent noon, and the difference 
between this and the Greemvich apparent noon is the 
difference of local times, or the longitude measured from 
the standard meridian. The final solution of this impor- 
tant problem depends therefore solely upon the perfection 
of the lunar tables, the moon, when once its movements 
are sufficiently understood to be accurately calculated 
beforehand, being as it were the hand of the clock to tell 
us Greenwich time all over the world. 



II. DENSITY OF THE EARTH. 

The dimensions of the earth have been accurately given 
in Chap. I., and from them its bulk is most readily 
calculable. It will be found to be 259,801 millions of 
cubic miles ; but before its absolute weight can be obtained, 
it is necessary to know the average weight of a cubic mile, 
or the mean specific gravity of its component matter. To 
find this, various experiments have been tried with more 
or less success. The most simple and obvious is to com- 
pare the attractive force of the whole earth with that of a 
mountain on its surface; and this is known from the 
mountain upon which the experiment was first tried, as 
the Schehallien experiment. This mountain is of tolerably 
regular form, and ranges east and west, and for these 
reasons is well suited for the purpose. Two stations — one 
on the north and the other upon the south side of the 
mountain — are selected, and by a triangulation similar to 
that explained in an early part of this work, the exact 
distance between them is obtained. Knowing, as we do, 
the length of the earth's radius, it is quite easy to find the 
angle that two radii drawn from the stations to the centre 
of the earth will form there. This angle will be none 
other than the true difference of latitude of the two 
stations. A zenith sector is next erected, and observations 
of certain selected stars near the zenith are made with it 



94 ASTRONOMY. 

successively at either station. This instrument consists 
of a telescope hanging from two pivots near the object-glass, 
and carrying at the lower or eye end a small graduated 
arc. Suspended from one of the pivots is a plumb-line, 
whose position, with reference to the graduated arc, 
measures the angular difference between the direction 
of a star and that of the zenith, as indicated by the 
plumb-line. When we have taken the differences of the 
zenith distances of each star, as found at the two stations, 
we shall have so many separate measurements of the 
difference of latitude, which will agree precisely with 
that obtained from the triangulation, provided that 
the direction of the plumb-line is accurately towards the 
centre of the earth. The centre of the earth is very 
distant, although its attraction is very powerful. The 
attraction of the mountain is very small indeed compared 
with it, but it is near, and so the plumb-line is slightly 
influenced by it, being directed a little towards the 
mountain when on either side of it. 

The difference of latitude, as found by triangulation, 
will therefore be less than that found by the zenith sector, 
and the amount of discrepancy will be twice the effect of the 
attractive force of the mountain upon the plumb-line. 
The next step consists in surveying the mountain in 
every direction, so that its bulk may be calculated, and 
specimens of the rocks of which it is formed must be 
taken. These are submitted to examination, and their 
density or specific gravity, compared with water, deter- 
mined. From these particulars, the absolute weight of 
the mountain will be found with some fair degree of 
accuracy, and the only question that remains is to find 
what weight must the earth be, that its attraction at the 
distance of its centre shall be such that the relative 
attractions of the mountain and it may bear the propor- 
tion to each other that the deviation of the plumb-line 
indicates. It was found that the average weight of the 
materials of the whole earth must be, bulk for bulk, 
nearly twice that of the rocks of Schehallien, or five 
times that of water, otherwise the deviation of the 



DENSITY OF THE EARTH. 95 

plumb-line, on account of the mass of the mountain, 
would have been greater than the amount observed. 

A second and somewhat similar method has also been 
employed. A pendulum that beats seconds truly at the 
sea level is carried to the top of a mountain, and its rate 
of going there is noted. The velocity of its vibrations 
depends upon the force of gravity acting upon it, which in 
this position may be regarded as two separate attractions — 
viz., the ordinary attraction of the earth at the sea-level, 
diminished by the increased distance from the centre; and 
secondly, the attraction of the mountain itself. The 
effect of the first on the pendulum is calculable from the 
law of gravitation, and the sum of the effects of both is 
observed; hence the difference gives the effect of the 
mountain's attraction. The structure of the mountain 
must be examined as before, and its density and weight 
determined ; and the attractive force of the earth, which can 
then be compared with that of the mountain, will be found 
similarly as in the preceding experiment. In this manner 
the general density of the earth has been again found to 
be about five times that of water. 

A third form of this experiment is to carry a pendulum 
down a deep mine, and there observe its rate of going. 
Newton has proved that the effect of gravitation in this 
situation is precisely as though a shell of a thickness 
equal to the depth of the mine had been everywhere 
taken off the globe, and that further its force would be 
diminished, supposing the earth to be formed of one 
density or material throughout in the proportion of the 
earth's radius to the radius minus the depth of the mine. 
When this experiment is made, it is found that the 
pendulum gains, which implies that the gravitation is 
greater there than at the surface; and hence the density 
of the interior of the earth is greater than that of the 
outer shell in a certain proportion, which the pendulum 
observations indicate. Of the density of the outer shell 
we can form a fair estimate; and hence that of the whole 
earth is determined. This experiment gives a rather 
greater density for the earth than the previous ones. 



96 



ASTRONOMY. 




We come, lastly, to the most important of these methods, 

which is known as the 
Cavendish experiment. 
In it a light beam of 
wood is suspended from 
k: : its centre by a fine wire, 
-;.-£} D E, and at either end 
a leaden ball of about 
2 inches diameter is 
fixed. When left to 
itself this balance will 
assume a place of rest, 
such that the wire is 
free from any torsion 
or twist. A telescope 
is then employed to 
Fig. 25. determine the exact 

position occupied by the balls. Two heavy balls, F, G, 
are now brought and placed very near the small ones, on 
opposite sides of the balance, and their attractions both 
tend to drag the small balls from the position of rest ; and 
this being resisted by the torsion of the wire, a very 
slow oscillatory motion is produced. The deviation from 
the previous position and the length of the oscillations is 
then measured by the telescope. The position of the 
spheres is then reversed by means of a turning frame, 
when they will occupy the points H, K, and the same 
measurements made. Yery great care has to be taken 
that no other effect than the attraction of the large balls 
is mixed up with the movements of the small ones, and 
the delicacy of manipulation of the observer is put to a 
most severe test. When the observations have been 
sufficiently repeated, the amount of the attraction of the 
large balls upon the small ones is ascertained. It is then 
a question of calculation, too intricate for these pages, to 
discover, if the earth was of the same general density as 
the balls, what would be the amount of the deviation and 
oscillation ; and as lead balls have been usually employed, 
it has been found that the average density of the earth is 



THE MOON. 97 

less than that of lead, in such proportion that 5*67 times 
the density of water will very nearly represent it. This 
is nearly the average of the five latest and most satisfactory 
determinations, and may be assumed to be very near the 
truth. The absolute weight of the earth is now a matter 
of simple arithmetic, as is likewise the weight of the sun 
or of any of the planets. 



III. THE MOON. 

The first example of a secondary planet or satellite 
which we meet with in the solar system, and by far the 
most important, is our own moon. It revolves (subject to 
great perturbations) in an ellipse with the earth in one of 
the foci, and with it is carried round the sun. Its orbit 
is only an ellipse with reference to the earth, being in 
fact a curved line, always more or less concave to the sun, 
when regarded as a movement in space. Yet we can 
separate the two motions completely, and regard its orbit 
round the earth as being performed in a strict ellipse, 
similar to the planetary orbits round the sun. Its mean 
distance from the earth, as before stated, is 238,851 miles, 
and the eccentricity of its orbit is rather greater than the 
earth's {^8^12)- ^ ^he P°^ n ^ where it is nearest to the 
earth, called the perigee, it is about 226,000 miles; when 
farthest from the earth, or in apogee, it is about 252,000 
miles distant. This variation of distance causes consider- 
able changes in its apparent size. At perigee it will be 
33' 31" in diameter, and at apogee only 29' 21". Its 
mean apparent diameter is therefore rather smaller than 
that of the sun, though it sometimes considerably exceeds 
and at others falls short of it. 

It must be understood that these measurements will 
only be correct supposing the spectator to be situated at the 
centre of the earth; for the moon, being comparatively 
near us, the distance of the centres of the earth and moon 
being only 60 terrestrial radii, it makes a sensible differ- 
ence in the apparent size of the moon, if the observer be 
situated so that he is nearer the moon by the length of 

A. G 



98 ASTRONOMY. 

the earth's radius. Thus, when the moon is on the 
horizon of any place it is nearly as far from the spectator 
as from the centre of the earth; but should it pass through 
his zenith, it will only he 59 radii of the earth distant 
from him, and hence will appear larger. This, therefore, 
forms a correction in lunar observations, and is known as 
the augmentation of the moon's semi-diameter. It 
increases in amount with the altitude of the moon, 
reaching a maximum at the zenith, should the observer 
be so situated that the moon passes through that point. 

The real length of its diameter is readily found from its 
apparent diameter and its distance, to be 2,160 miles, or but 
little more than J that of the earth. From this it follows 
that the earth viewed from the moon will appear 13| 
times the size that the moon appears to us. It will also 
be found that the bulk of the moon is only -£§ that of the 
earth. 

Notwithstanding the most careful observations having 
been made, no ellipticity of form or polar compression has 
been discovered. There are, however, some reasons which 
may lead us to suppose that the moon is not perfectly 
spherical. It has been suggested that it may be slightly 
egg-shaped, the thin end being turned towards the earth. 
The centre of gravity of such a mass would be towards 
the side which is removed from the earth; and if this 
supposition is made, a curious fact connected with the 
rotation of the moon is partly explained. Moreover, if 
the moon had been at one time in a fluid state, with 
motions something similar to those it now has, tlie attrac- 
tion of the earth would have tended to produce this form. 

The orbit in which the moon revolves is inclined to the 
ecliptic at an angle of 0° 8' 48", and the moon may attain, 
therefore, a more considerable altitude than the sun does 
in summer by this amount, or it may be to an equal 
amount at a less altitude than the sun at the winter 
solstice. Connected with this is the explanation of the 
peculiarities of the harvest moon. This is a name given 
to the full moon that happens nearest the autumnal 
equinox (viz., Sept. 23). On this elate the full moon, being 



THE MOON. 99 

opposite the sun, is at the vernal equinox in Aries, and at 
its rising the whole of the southern portion of the ecliptic 
is above the horizon and to the west of the moon. Its 
motion being from west to east, it will day after day reach 
a higher north declination; and although ordinarily it 
rises almost an hour later each day, it will in consequence 
of its increasing north declination at this time rise nearly 
at the same hour for several evenings together near full 
moon. Its light is thus often useful in harvest operations. 
Should this moon, when full, be in the ascending node of 
her orbit, the increase of declination will be very rapid, as 
the inclination of her orbit to the ecliptic will be added to 
that of the ecliptic to the earth's equator; and in latitudes 
but little north of Britain, this will lead to the moon's 
rising even earlier each succeeding day for a short time. 
On the contrary, should this full moon be at the descend- 
ing node, it will only be the difference of the two inclina- 
tions that will carry the moon north, and the peculiarity 
respecting the rising of the harvest moon will be less 
noticeable. It should be mentioned that in every lunation, 
when the moon is at this point, a similar fact may be ob- 
served regarding its rising; but not being at the full phase, 
it is not so much noted. 

The length of the moon's sidereal period is 27 days 7 h 43 m 
1 1 "5 s - The lunar month or lunation is the synodical period 
of the moon, or the time elapsing between one conjunction 
and the next, which, for the reason already explained in 
the case of the inferior planets, is more than one complete 
revolution. The length of the lunation is 29 days 12 h 44 m 
2 -87 s . Twelve lunar months, or 354*367 days, is often 
called the lunar year; and as the difference between this 
and the tropical year is eleven days, it follows that the 
moon is eleven days older at the beginning of each suc- 
ceeding year. The accumulation of this number of days 
each year, from which the length of a lunation must be 
subtracted, if it should exceed a lunar month, is called the 
enact of the year. This is of great use in finding Easter. 
Also, 235 lunar months, or 6,939*69 days, are very nearly 
equal to nineteen ordinary years. This is called the 



100 ASTRONOMY. 

Metonic Cycle, and is likewise used for finding Easter, as 
well as for correcting the calendar of those nations who 
use the lunar year. 

A very singular fact is connected with the revolution of 
the moon on her axis, and seems to be a law which all 
secondary planets obey. The time of its rotation is 
precisely the same as the time of its revolution round 
the earth, or sidereal period; and in consequence of this 
fact the moon always turns the same side towards us. If 
the moon be egg-shaped, as has been supposed, the earth's 
attraction would tend .to keep the thin end always 
turned towards her, since that part would be nearer than 
the other, and would be attracted more powerfully in the 
proportion of the squares of the distances. The axis of the 
moon's rotation is but little inclined from perpendicularity 
to the ecliptic, the plane of its equator making an angle 
of 1° 32' with the plane of the earth's orbit, or about 
6° 41' with the plane of her own orbit. Now, if the 
axis of the moon's rotation had been exactly perpendicular 
to the plane of her orbit, it is clear that the lunar poles 
would have been always situated at the margin or limb of 
the moon as it is seen from the earth; but since it is 
inclined at an angle of 6° 41', it follows that sometimes the 
north and sometimes the south pole is turned towards the 
earth to this extent. It is, therefore, not strictly true 
to say that the same face of the moon is invariably turned 
to us, for we are able to see at times a small portion — viz., 
in the vicinity of the poles — of the side usually turned 
from us. The name of libration in latitude is given to 
this phenomenon. 

There is, however, another kind of libration which 
enables us to see a still greater portion of the opposite 
side of the moon. It arises from the fact that the lunar 
orbit being sensibly elliptical, the moon's daily motion will 
vary considerably, being now faster and now slower. Its 
rotation on its axis is, however, performed uniformly, and 
thus the two motions do not keep pace throughout the 
whole revolution, but the one will for a time gain upon 
the other, and then lose. For example, take a quarter of 



THE MOON. 101 

the lunar orbit near apogee, which will be described more 
slowly than with a mean velocity, and will therefore take 
a longer interval than a quarter of the sidereal period. 
In this time the rotation will have executed more than a 
quarter of its revolution, or the moon will be more turned 
on its axis, than is compensated for by the orbital move- 
ment. This is called the libration in longitude, and by it 
we are enabled to see a few degrees on either side of the 
equatorial parts of the moon. There is yet one other but 
much smaller libration, which arises from the position of 
the observer upon the surface of the earth. If the moon 
be rising or setting, it will plainly be possible for us to see 
a small space round the moon's border, which we cannot 
see when she is on the meridian. This is known as the 
diurnal libration. From the combination of all three 
phenomena we are able at one time or another to see 
about ^ of the moon's surface. Of the remainder we can 
have no knowledge whatever. 

The mass of the moon is by no means so readily found as 
that of the earth. Satellites are always extremely useful in 
determining the mass of their primaries, the method being 
as easy as it is accurate; but the reverse problem, that of 
finding the mass of the moons, from the disturbances they 
effect upon the planet round which they revolve, is more 
difficult. As we have not yet spoken of perturbations 
generally, we shall content ourselves by saying that there 
are no less than four ways in which the moon's mass may 
be found. The attractions of the sun and moon cause 
slight motions of the earth's axis, tides on the ocean, &c; 
and by apportioning these into two parts, separating what 
belongs t6 the sun's attraction from what belongs to the 
moon's, we may obtain a knowledge of their relative 
attractive forces, or their masses. It has been found that 
the moon's mass is about ~^. T or '012285 that of the earth ; 
and since we have already found its bulk to be -^ of the 
earth's, it follows that the density can only be about 5-, 
the earth's density being unity, or 343 times as heavy as 
water. From the lightness of its matter, as well as from 
its small size, the force of gravity upon the surface of the 



102 



ASTRONOMY. 



moon will be very small — not more than |- of the gravity 
on the earth's surface. In other words, a pound of lead 
at the earth's surface, if transported to the nioon, would 
weigh but 2f oz., and the muscular energy of a man would 
be increased sixfold for the same reasons. 

Like all other bodies of the solar system, the sun ex- 
cepted, the moon shines only by reflected solar light; and 
since it revolves round the earth, the variety of positions 
it assumes with reference to the two bodies must give rise 
to phases like those of the inferior planets. Fig. 26 re- 
presents eight several positions of the moon during her 
synodical revolution round the earth, T; the dotted lines 
indicating the nearly parallel direction of the solar rays 
upon either body, and the small circles the lunar phase. 
At A, the moon is in conjunction, the unenlightened 
hemisphere is wholly turned towards T : it is therefore 
invisible, or we have new moon. At C and G, one half 
of the hemisphere turned towards T is illuminated by the 
sun, and these are the first and last quarters; the moon is 
also said to be in quadrature at these points. Between 
them and conjunction, positions B and H, the moon will 




be a crescent, but evidently the horns will be turned in 
opposite directions, as seen from T — viz., at B, to the left 
hand, or east; and at H, to the right hand, or west. At 
E, or in opposition, the whole of the face towards the 
earth will be bright or full, and between opposition and 



THE MOON. 103 

quadratures the moon will be gibbons. The points of 
conjunction and opposition are called the Syzygies, a term 
only applied to the moon; and points midway between the 
syzygies and quadratures are sometimes called Octants. 

Notwithstanding the moon's brightness, she reflects but 
a small portion of the sun's light incident upon her. It 
has been estimated that she absorbs or retains for her own 
use nearly J- of the solar rays, reflecting only the remainder, 
or not more than would be reflected by " grey weathered 
sandstone rock." Some of the planets reflect far more 
than the moon— the albedo or reflecting power of Mars 
being J of the incident light, of Saturn J, and of Jupiter 
nearly |-. The cloudy atmosphere of the latter planet 
must therefore be nearly as brilliant as white paper. The 
earth, in like manner, reflects the solar light; and to the 
moon exhibits phases exactly complementary to hers, or 
being full when the moon is new to us, &c. The light 
which the earth reflects must be very considerable, and 
near the new moon, the earth being gibbous, as seen from 
our satellite, the earth-shine is again reflected back to us. 
At these times the entire outline of the moon is visible, 
part brightly illuminated by the sun, and the rest faintly 
by the earth. It is commonly enough seen thus in the 
twilight sky. As the moon's phase increases, however, 
the earth's decreases, and the earth-shine is not visible far 
from the new moon. 

That our satellite is destitute of any sensible atmosphere 
is shown by a variety of facts, particularly by the absence of 
any twilight upon the borders of its darkened hemisphere, 
and by the sharpness of its shadows. Other phenomena, 
the effects of refraction, would also be noticed — as, for in^ 
stance, a bright line round its border during a solar eclipse ; 
but a more delicate test than either of these is found in 
the observation of occultations. The moon in her monthly 
course occasionally passes our fixed stars, and these are 
found invariably to disappear with astonishing suddenness 
upon touching the limb of the moon, emerging after an 
interval in a similar manner on the other side. Now, had 
the moon any atmosphere at all comparable in density 



104 ASTRONOMY. 

with the earth's, stars would be found to fade as their light 
passed through it, when close to the limb. It is therefore 
certain that there is no lunar atmosphere of any extent, 
and, by a necessary consequence, neither water nor clouds 
can exist upon its surface. The lunar day, which is like- 
. wise the lunar summer, will be nearly 15 days' duration; 
and during its continuance, the heat of the sun will be 
unmitigated in any way, resulting in a temperature far 
greater than that of the hottest African desert, where 
water, supposing it to exist, would be at once evaporated. 
The lunar night, of equal duration, will be far more in- 
tensely cold than is ever experienced on the earth. In 
these violent extremes vegetation will be impossible, and 
the surface must be alternately burnt up and frozen. Yet, 
notwithstanding the high temperature of the illuminated 
portion, none of the heat is reflected to the earth ; or, if it 
is, must be absorbed in the higher regions of our atmo- 
sphere. Recent observations, it is true, show that by the 
most delicate apparatus some minute portion of heat is 
measurable; but it is far too small to have any effect on 
terrestrial temperatures. It has, indeed, been noticed that 
there is less cloud near the time of full moon, but that this 
is an effect of reflected heat, has not been fully made out. 
When examined by the telescope, the surface of the 
moon is found to be very diversified. High mountains 
exist which throw long black shadows, especially when 
near the terminator — that is, the extremity of the en- 
lightened hemisphere, or the line that indicates sunrise 
and sunset on the lunar surface. From the lengths of these 
shadows, the heights of more than a thousand of these 
mountains have been measured. The highest peaks reach 
to nearly 23,000 feet, or -^^ of the moon's diameter, and 
are therefore comparatively three times as high as those 
on the earth. That they have been raised by volcanic 
agency appears certain, from the form assumed by most of 
them — namely, immense crater-like basins, of which the 
interiors are often much lower than the general outer sur- 
face, and having near the centre of the basins a steep 
conical hill. Though on an immensely larger scale, they 



ECLIPSES. 105 

present the exact conformation of terrestrial volcanoes; 
but there is no evidence of there having been any active 
volcanic agency at work since the invention of the tele- 
scope. The numerous craters are almost invariably circular, 
or fore-shortened into ellipses, near the moon's limb. The 
broad tracts called seas are not really oceans, for the 
reasons before stated : they are probably more allied to our 
alluvial plains, and their less reflective power is to be 
attributed to general roughness of surface. 



IV. ECLIPSES. 

The sun being the only source of light in the solar system, 
and all the planets, as well as their satellites, opaque bodies, 
it necessarily follows that each casts behind it a long conical 
shadow, and that if, in the course of their revolutions, any 
two bodies come into the same straight line with the sun, 
that luminary will be wholly or partially hidden from the 
body most remote from it, which will therefore be more or 
less incapable of reflecting light. Hence arise various 
jDhenomena, of which the eclipses of the sun and moon are 
the most important. The theory of an eclipse of the moon 
is very simple, as will be seen from the accompanying 
diagram. If S represent the sun, and E the earth, the 
dimensions of the earth's shadow will depend upon the 
diameters of the two bodies, and their distance from each 




Fig. 27. 

other, being determined by the lines A a and B b. The 
distance of the apex of the cone, C, will vary slightly, 



106 ASTRONOMY. 

owing to varying distance of the earth from the sun, but 
it will never exceed 220, nor fall short of 212 terrestrial 
radii. It always reaches, therefore, far beyond the lunar 
orbit. There exists also a partial shadow outside the 
conical limits, abC; for, if we draw the lines B a and A 6, 
and produce them beyond the earth to D and G, it is 
clear that the sun would be partially hidden or eclipsed to 
any spectator within the space D a C or C b G-, as it is totally 
eclipsed to a spectator within the cone a C b. This in- 
verted truncated cone is called the penumbral shadow; and 
it will deepen in intensity of shade as we approach the 
umbra or perfect shadow, because the nearer a spectator 
is to the cone, a C b, the greater will be the portion of the 
sun hidden from him. 

If the moon in her monthly orbit, m m r , pass centrally 
through this shadow, she will first enter the penumbra, 
which will gradually deepen as she proceeds, and after- 
wards be totally eclipsed in the umbra, and emerge finally 
after passing the penumbra again. If the moon only pass 
through the penumbra without touching the true shadow, 
it is not regarded as an eclipse, or a part of the disc only 
may be enveloped in the earth's true shadow, in which 
case the eclipse \s partial. From the position of the earth 
and moon, it will be seen that a lunar eclipse can only 
take place when the moon is in opposition or full. 

The cone of shadow cast by the moon is of course very 
much smaller and shorter than the earth's. Though at 
the time of new moon or conjunction, if the moon be 
at or near the ecliptic, it is directed towards us, it 
may or may not reach the earth, according as the moon is 
near her perigee or apogee. In the former case, the sun 
will be totally hidden from some portion of the earth; aiid 
in the latter, the moon's disc being too small wholly to 
cover the sun, a narrow ring of light will be left all round 
the moon at the moment that the centres of the two 
bodies coincide in direction. Such an eclipse is called 
annular. 

The theory of solar eclipses is shown in figs. 28 and 29, 
where E represents the earth and M the moon. The 



ECLIPSES. 



107 



direction of the solar rays is indicated by the lines S m 
and S m' from the upper border of the sun, and by S' m 
and S' m from the lower border. It will be seen that the 




Fig. 29. 

diameter of the shadow cone, when it reaches the earth is 
very narrow, under the most favourable circumstances not 
more than 180 miles, which is the extreme limit of the to- 
taiiitj of an eclipse. The penumbra is limited to a circle of 
4,900 miles diameter, beyond which there will not be even 
a partial eclipse. In consequence of the earth's rotation, 
it must be remarked, the cone of shadow traverses a con- 
siderable distance over the earth's surface; and the limits 
given above are those at any instant of time, or they 
express the breadth of the zone which is thus traversed by 
the shadow. In fig. 29 no part of the shadow touches the 
earth, and it is only near the centre of the penumbra, on a 
line joining the centres of the sun and moon, that an 
annulus will be formed round the latter body — elsewhere 
the eclipse will be partial. 

It will appear from what has been said that the total 
phase of a solar eclipse is seen only from a very small 
portion of the earth, and even as a partial eclipse is not 
visible over a whole hemisphere. On the contrary, lunar 



108 



ASTRONOMY. 



eclipses are seen over a much wider range. Thus, if m 
(&g. 30) represent the position of the moonwhenit enters the 
earth's shadow, and if its motion, together with the diur- 
nal movement of the earth bring it to m' when it emerges 
from it, and at these times it is vertical over the points a 
and b of the earth's surface, then the limits of its visibility 

will be determined by the 
rational horizons of the two 
places — namely, a a" and 
b'b\* Within the limit 
b' E a b the eclipse will be 
visible throughout its whole 
duration, and the whole or a 
part of the phenomena will 
be seen within the limits 
a'W)"b, or more than a 
hemisphere. If the moon's 
motion round the earth were 
performed in the plane of 
the ecliptic, there would 
plainly be a lunar eclipse at 
each full moon or opposition, 
and the moou would pass 
between the sun and earth, 
causing a solar eclipse at 
Fl £- 30 - each conjunction or new 

moon, but such is not the case. The lunar orbit, we 
have already stated, is inclined more than 5° to the ecliptic; 
and hence eclipses, either solar or lunar, can only take 
place when the moon is very near the ecliptic — i.e., near 
her node, at the same time that she is at either conjunc- 
tion or opposition. To find at what distance from the 
node the sun and moon may be, and yet a lunar eclipse 

* The rational horizon of any place is a plane parallel to the 
sensible horizon, and passing through the centre of the earth. Its 
intersection with the earth is a great circle, of which the position 
of the observer is the pole. At the almost infinite distance of the 
fixed stars the rational and sensible horizons are to be regarded as 
the same, for which reason no distinction has hitherto been made 
in this work between them. 





ft "^ 



Fij?. 31. 



THE MOON. 109 

take place, it is necessary to take into account the diame- 
ter of the earth's shadow at the distance of the moon, and 
the apparent diameter of the latter body. Thus, if SES' 
(fig 31) represent a section of the earth's shadow cone at 
the distance of the moon, the centre of which necessarily 
falls on the ecliptic E N, and M, the moon, moving along 
her orbit, M N P, of which N is the node, then the 
greatest distance at 
which an eclipse 
can occur is deter- 
mined by the point 
at which these two 
circles touch one an- 
other. It is found 
by solving the tri- 
angle, MNE, for the 
greatest and least 
values of EM — that is, when the moon is in perigee (E S, the 
radius of the earth's shadow, and S M, the radius of the 
moon, being then greatest), and in apogee when they are 
least — that an eclipse may take place, if at the moment of 
opposition the moon is not distant from one of her nodes, 
and the sun from the other more than 12° 24', and that if 
nearer than 9° 23', a lunar eclipse is sure to occur. These 
points are called the greatest and least lunar ecliptic limits. 
In determining the like points for a solar eclipse visible 
at any part of the earth, we have to take into account the 
apparent diameter of the sun as well as that of the moon; 
and hence the solar ecliptic limits are greater than the lunar. 
It is found that a solar eclipse may take place, if, at the 
moment of conjunction, the sun and moon are not more than 
18° 36' from either node; and that if less than 15° 20', an 
eclipse visible somewhere upon the earth is certain. It will 
be concluded, therefore, that in a given time the number of 
solar eclipses will be greater than the number of lunar, the 
proportion being as 41 to 29; but, in consequence of the 
more extended range of visibility of the lunar eclipse, 
there will usually be visible at any one place nine lunar 
eclipses to four solar. 



110 ASTRONOMY. 

If the lunar nodes were fixed, or nearly fixed points, the 
sun would be in the same direction twice a year — once at 
either node — and the occurrence of an eclipse would 
simply depend upon the fact, whether the moon was in 
opposition or conjunction during the time that the sun 
was within the limits already assigned. Eclipses would 
then always be confined to particular months. The 
nodes have, however, a very rapid motion of retrogres- 
sion; and hence the sun comes into the direction of the 
same node in less than a year, or in 346-6194 days. Now, 
if this were an exact multiple of the moon's sy nodical 
period, and an eclipse once took place, it would recur 
again and again at this interval of time; and although 
this is not so, something very similar happens. It is 
found that nineteen such periods, or 6,585*772 days, are 
very nearly equal to 223 lunations, or 6,585*321 days, from 
which it follows that at the end of this period the sun, 
nxoon, and lunar node are in the same relative positions 
as at the beginning, and that all the eclipses that 
take place within the period will recur again in the same 
order after the lapse of 6,585 *321 (lays , or 18*™- ll days 7 h 
43 m * 

The knowledge of this period and its use in predicting 
eclipses is very ancient, and was known to the Chaldeans, 
who gave it the name of the Saros. In it there are 
usually seventy eclipses, and as many as seven may occur 
in one year; the usual number will be four: but two only 
may occur, in which case they will both be solar eclipses. 
As many as five solar eclipses may occur in one year, but 
never more than three lunar. This arises from the great 
extent of the solar ecliptic limits, so that one conjunction 
must, and two may take place, while the sun is within 
the required distance on one side or the other of the node. 
Hence two solar eclipses, one at either node, must occur 
each year, and four may so occur. Should the first of them 
take place very early in the year, a fifth may happen very 

* This period will be 18y rs - ll da y s 7 h 43 m , or 18^ s - 10 da ^ 
7 h 43 m , according as four or five leap years are included in the 
interval. 



THE MOON. Ill 

late, the synodical revolution of the node being less than 
a year by nineteen days. 

But since 223 lunations are not precisely equal to 19 
synodical revolutions of the node, a slight irregularity 
arises. The difference is nearly 10| hours, and in this 
time the node will have moved, with reference to the sun, 
28' 6", a space that in the lapse of about seventy-nine 
eclipse periods will carry the node completely through the 
greatest solar ecliptic limits. The effect of this upon solar 
eclipses is, that at each repetition they occur rather 
more southerly than before, till at last they disappear 
altogether off the earth at the south pole. 

It will appear from what has been said that total solar 
eclipses at any particular spot of the earth's surface are 
very rare occurrences. No solar eclipse has been total in 
London between a.d. 1140, and a.d. 1715, nor has 
there been one since the latter date, though there have 
been several annular eclipses. It is this that renders the 
record of' ancient eclipses invaluable in chronology, as 
they are also tests of the accuracy of our lunar tables. 
'Now that the motions of the sun and moon are perfectly 
accounted for, we can trace back and calculate when and 
under what circumstances an eclipse occurred. For in- 
stance, the eclipse of Thales, named from the philosopher 
who predicted it, happened when the Medes and Lydians 
were engaged in battle ; and in consequence of it a peace 
was concluded. The date of this event is fixed with the 
utmost certainty, by the fact that an eclipse did take place, 
which was total from the site of the battle, upon May 28, 
585 B.C. In similar manner, the Persians took the city 
of Larissa (the modern Ximroud) while the inhabitants 
were alarmed by a total eclipse of the sun. This date is 
determined to be May 19, 557 B.C., from the fact, that 
an eclipse was total there on the date mentioned. Many 
others have been similarly fixed, the earliest of all being 
an eclipse recorded in Chinese annals of the date October 
13, 2128 B.C. It is probable that the Chaldean Saros was 
known even at that remote date. 

The phenomena which occur at a total eclipse of the sun 



112 ASTRONOMY. 

have been briefly noticed in the preceding chapter, and it 
only remains to notice the peculiarities of a lunar eclipse. 
Though totally immersed in the earth's shadow, it is but 
rarely that the moon is not visible to us, and it generally 
assumes a dull red or copper colour. The explanation of 
this fact is found in the refraction of the rays of the sun 
in passing through the terrestrial atmosphere, which 
absorbs the blue rays largely and transmits only the red 
and yellow, precisely as occurs at a rosy sunset. The 
red light thus bent in, encroaching on the earth's shadow, 
is sufficient to allow the moon to be seen; but its amount 
will vary in different eclipses on account of the different 
states of the atmosphere. There are instances on record 
of the moon being completely hid, in which case the zone 
of atmosphere through which the rays were refracted 
must have been heavily laden with clouds and moisture. 
At other times the brightness of the illumination has been 
snch that the eclipse would almost have been questioned, 
but for the deep red colour, resembling that of a bright 
cloud at sunset. 

QUESTIONS. 

1. By what amount may the earth's distance from the sun 
vary ? When is the earth in perihelion ? When in aphelion ? 

2. Explain the position of the earth's poles with reference to 
the sun at the equinoxes aod at the solstices. 

3. What two causes combine to produce the heat of summer ? 
Explain how they tend to do so. 

4. What is the effect of the earth's varying distance from the 
sun upon the heat of the southern summer and the northern 
winter ? 

5. Are all the seasons equal in length? What causes the 
inequality ? 

6. How is the latitude of any place on the earth found? 

7. How is the differeuce of longitude of two places found, if both 
are on land? State some methods that may be employed to 
compare local times. 

8. Explain how the moon is employed to find the error of a 
chronometer, or to show Greenwich time at any point of the earth. 

9. How may the local time at any place be found ? Shew that 
this gives us the longitude. 

10. Give the bulk of the earth in cubic miles. 

11. What is the principle of the Schehallien experiment? Ex- 



QUESTIONS. 113 

plain the various steps by which it leads us to a knowledge of the 
earth's mean density. 

12. Describe the zenith vector and its use. 

13. Give the result of the Schehallien experiment. 

14. In what other way may the attraction of a mountain be 
employed to find the density of the earth ? 

15. What does the law of gravitation teach us of the effect of 
gravity down a mine ? Under what circumstances will it be greater 
and less than at the surface ? 

16. How has this been employed to find the density of the earth? 

17. Describe the apparatus used in the Cavendish experiment. 

18. With what final result has this experiment been made ? 

19. Explain the moon's motion with reference to the earth ; also 
with reference to the sun. 

20. What terms are applied to the points of nearest approach 
and greatest distance from the earth ? By what amount do they 
differ? 

21. What are the limits to the variation of the moon's diameter? 
Compare with the sun's. 

22. What is meant by the augmentation of the moon's semi- 
diameter ? Explain the cause of it. 

23. Give the actual diameter of the moon, and compare the 
dimensions and bulks of the moon and earth. 

24. State what is known or suspected of the moon's form. 

25. At what angle is the lunar orbit inclined to the ecliptic? 

26. Explain the peculiarity of the harvest moon. 

27. Give the sidereal and synodical periods of the moon. 

28. What is meant by a lunar year? What by the epact ? 
What is the Metonic cycle ? 

29. Give the time of the moon's rotation ; and why do we 
see but one side of it? 

30. At what angle is the moon's equator inclined to the ecliptic, 
and also to the plane of its own orbit? 

31. What is meant by libration in latitude ? 

32. What causes libration in longitude? What the diurnal 
libration? Sum the effects of the three librations. 

33. State generally the means adopted to find the mass of the 
moon. Give it and likewise its density, and the effect of 
gravity on its surface. 

34. Trace the lunar phases through a synodical period. 

35. Explain the terms lunation, quadrature, syzygy, albedo, 
octant. 

36. Give an illustration of the brightness of the moon compared 
with terrestrial matter and the planets. 

37. What phases does the earth present to the moon? What is 
the earthshine, and why is it only seen near the new moon ? 

38. From what phenomena is the absence of atmosphere on the 
moon proved, and what effect must result as regards temperature ? 

A, H 



114 ASTRONOMY. 

39. What is known and conjectured about the reflection of beat 
from the moon ? 

40. Give a general description of the lunar surface, and state 
what is meant b}^ the terminator. 

41. What are the usual characteristics of a lunar crater, and 
give the general height of the mountains compared with those of 
the earth. 

42. State the general cause of eclipses. 

43. Give the length of the earth's shadow, and the meaning of 
the terms umbra, penumbra. What is the degree of shade in the 
penumbra ? 

44. State the general conditions of a solar eclipse. Distinguish 
betweeu annular and total eclipses. Whence do the two varieties 
arise ? 

45. Give the extreme limits of visibility of a total and partial 
solar eclipse, and state the effect of the earth's rotation on these 
limits. 

46. By what is the visibility of a lunar eclipse determiued? 
Explain the term rational horizon. 

47. At what points of the lunation must eclipses respectively 
occur, and why not at every conjunction and opposition? 

48. What are the greatest and least luoar ecliptic limits? Ex- 
plain the term. 

49. Give the solar ecliptic limits, and the reason why they 
exceed the lunar. 

50. Give the proportion of solar and lunar eclipses generally, 
and for any one place upon the earth ; also the cause of the 
difference. 

51. State the length of a synodical revolution of the node. Why 
does it differ from an ordinary year ? 

52. Explain the reason of the recurrence of eclipses after 
eighteen years. 

53. State the usual number of eclipses that occur in the Saros, 
and the number of either kind that may happen in one year. 

54. What irregularity is there in the recurrence of eclipses, and 
how many times may an eclipse recur? 

55. Explain and give illustrations of the use of ancient eclipses 
in chronology. 

56. What is the cause of the redness of the moon in lunar 
eclipses? Explain why the redness varies. 



115 



CHAPTER VI. 

SUPERIOR PLANETS. 
I. MARS. 

Of the planets revolving round the sun exterior to the 
earth, Mars is the nearest to it, and is in very many 
respects a most interesting planet. It was the considera- 
tion of its varying brilliancy, which is sometimes equal to 
Jupiter, and at others hardly equals a second magnitude 
star, that led Copernicus to reject the earth as its centre 
of motion, and transfer that point to the sun; and it was 
also from the rigorous examination of the motions of this 
planet that Kepler established his celebrated laws, which 
he extended by analogy only to the other planets. 

Being a superior planet, it does not remain in constant 
attendance upon the sun; for it is evident that the earth 
may come between it and that luminary, when the two 
bodies must necessarily be in opposition to each other. 
Its distance from the earth at different times will vary to 
the extent of twice the earth's distance from the sun, and, 
indeed, owing to the great eccentricity of Mars' orbit, to 
even a greater amount than this. Its apparent diameter 
will similarly be liable to very extensive changes, the 
limits of its variation being 30"4 and 4"*1. Its real dia- 
meter has been found to be 4,920 miles, or J- of the earth's. 
It is therefore the smallest planet in the system, after 
Mercury. Its mean distance from the sun is 139,312,000 
miles ; but owing to the eccentricity being great (yoVx )> 
second only to Mercury in this respect also; its perihelion 
distance is about 126, and aphelion distance 152 millions 
of miles. To make one complete revolution in this orbit 
it requires very nearly 687 days; but for its synodical 
period, requires 780 days, during 73 of which it is retro- 



116 



ASTRONOMY. 



grading.* It has thus the longest synodical period of any 
planet, and in consequence is most rarely seen, the inter- 
vals of its appearance in opposition, as stated above, being 
two years seven weeks. Further, it is the only one of 
the superior planets that present any perceptible phase. 

This arises from the fact that 
the others are so distant that we 
view them very much as they 
would be seen from the sun. 
The phase of Mars never ex- 
ceeds a slight gibbosity, seven- 
eighths of its disc being always 
illuminated. Fig. 32 shows the 
position of the earth and Mars 
when the latter presents its 
least possible phase* — namely, 
when the earth is at its greatest 
elongation, as seen from Mars, 
and presents to it only a half- 
moon. At the points C and 
O, which represent the position 
of the earth when Mars is in con- 
junction and opposition, it is 
evident that the latter will be 
full, as seen from the former. 
To ascertain the mass of this planet, it having no satel- 
lite, has been as difficult a problem as that of Mercury; 
but it has been fixed, from the disturbances it effects upon 
the earth, to be ■£,TTWG,'tt7 that °f ^ e sun - Its mean 
density, using this evaluation, will be scarcely half that of 
the earth, or 2*82 times the specific gravity of water. 
Also, the effect of gravity on the surface will be found to 
be only -304 of the earth's gravity; in other words, a pound 
weight taken to the surface of Mars would weigh there 
five ounces only. 

Unlike the planets, of which we have already 
spoken, the surface of Mars is very distinctly marked, 

* The retrograde movement of the superior planets occurs always 
at the time of opposition, and for an interval on either side of it. 




Kfc 32. 



MARS. 117 

offering many spots favourable for determining its period 
of rotation. This has therefore been found with great 
accuracy, as well as the direction of the axis round which 
it revolves. The most recent calculations give a period 
of 24 h 37 m 22'735 3 for its rotation, and the inclination 
of the equator to the plane of the ecliptic as 28° 51/. 
From both these facts we see how nearly the conditions of 
climate must agree with our own; for, although the sea- 
sons will differ greatly in duration both among themselves, 
owing to the great eccentricity of the orbit, and from the 
earth's, owing to the much greater length of Mars' year, 
still the distribution and variation of heat over the surface 
must agree very closely with what we know to be the case 
with the earth. 

This is still further confirmed by the presence of two 
brilliant white patches near the poles, which can be none 
other than masses of snow and ice, since they are seen in 
diminish as the Martial summer comes on in either hemi- 
sphere, and increase during the Martial winter. More- 
over, since these patches are not of greater relative 
extent than exist' on the earth, it follows that Mars must 
enjoy a similarly temperate climate. Yet the intensity of 
the sun's light and heat there will be only f- of that upon 
the earth — showing that there must either be a dense 
atmosphere, capable of retaining the solar heat better than 
our own, or that the soil and matter of the planet absorbs, 
but does not so readily part with the heat radiated upon 
it. That there does exist an atmosphere is clearly indi- 
cated by the presence of the snow at the poles, as well as 
by other phenomena ; but that it is very dense or extensive 
has been denied. 

Permanent markings and conspicuous diversity of colour 
upon the disc of the planet clearly indicate the existence 
of continents and seas; but, curiously enough, the larger 
portion of the surface would appear to be land. These 
parts always appear of a reddish tint in the telescope, and 
give rise to the fiery appearance of the planet to the naked 
eye. We must suppose that this is the real colour of the 
soil; and it is probably something like the red sandstone 



113 



ASTRONOMY. 



districts on our own globe. The seas have a greenish or 
bluish-grey colour; but, owing to the preponderance of 

land, the general colour 
of the planet is red. 

Much controversy has 
been held upon the sub- 
ject of the polar com- 
pression of Mars, it 
having been set down 
very variously by dif- 
ferent observers. The 
latest determination 
seems to be the most 
trustworthy, and is 
nearly the mean of the 
best previous measures. 
The result is an ellip- 
ticity of 3-f F , or, equa- 




Ksf. 33. 



toriai diameter, 4,920 miles; polar diameter, 4,789 miles. 



II. THE ASTEROIDS 



The zone of small planets situated between Mars and 
Jupiter form a group of bodies remarkable in very many 
respects. Their existence, though suspected in the last 
century, was not actually discovered till the commence- 
ment of the present, when a systematic search was made 
for them, to be rewarded by the discovery of four new 
planets in the space of a very few years. A long interval 
then intervened, and no more were found till the year 
1845, since which elate each succeeding year has added to 
the number. As many as 125 are at present known, and 
have their orbits calculated. It was an hypothesis of 
Olbers, one of the earliest successful searchers for them, 
that a large planet had been exploded or broken to frag- 
ments by a concussion, and that very numerous members 
would be found. This supposition, though to some extent 
verified, is now pretty generally rejected; yet the minute 



THE ASTEROIDS. 119 

• 

bodies evidently belong to one family, for they involve in 
orbits so entangled that it has been said that, if the orbits 
be imagined as material rings, the whole could be suspended 
by taking any one up at random . It is more probable that 
this zone of planetoids form a connecting link between the 
large planets and the streams of meteors, and that they 
have been at one time a mass of matter resembling the 
rings of Saturn; but, owing to their insignificant mass and 
great distance from the sun, the equilibrium has been lost, 
breaking up the ring, and forming a number of bodies re- 
volving each. in its own separate orbit. 

With the exception of the diameters of one or two of 
them, which have with difficulty been measured, little is 
known of their size or weight. The largest are Ceres and 
Vesta — two of the earliest discovered. If we suppose all 
the planetoids equally to reflect the solar light, we may 
arrive at a very fair estimation of the magnitudes of the 
others from the consideration of their relative brilliancy 
and their distances from the sun and from the earth. In 
this manner it has been found that they most probably 
vary in size, from the superior limit of 228 miles in 
diameter to about 15 miles, the magnitude of the smallest 
yet known. Vesta is occasionally seen with the naked 
eye, but the others are very much fainter; and there is a 
well marked decrease in brilliancy and size to be ob- 
served in the more lately discovered planets. It would 
appear, therefore, that though the number of them is 
probably unlimited, yet the larger are nearly all known, 
and that the optical power of the telescopes now in use 
will gradually set a limit to the discovery of more of the 
group. It is known that the total mass of all the asteroids 
must be insignificant, and taken together they would not 
form a body of the size of Mercury. 

Their orbits are frequently much more inclined to the 
ecliptic than those of the larger planets; and hence they 
have sometimes been termed ultra- zodiacal. Pallas is the 
most inclined of any, the inclination of its orbit being 
34° 42', or five times the inclination of Mercury. The 
eccentricity of the orbits is also usually greater, many of 



120 ASTRONOMY. 

them exceeding Mercury in this respect also. Their mean 
distances from the sun vary greatly • that of Flora, which 
is the nearest to it of any, is only 201,273,000 miles, and 
its sidereal period is 1,193 days, or 3 J years. Camilla 
revolves at a mean distance of 325,509,000 miles, and its 
period is 2,453*6 days, or 6| years. These may be taken 
as very near the extreme limits of the zone. 

It is possible to learn but very little of the physical 
constitution of these minute bodies. One or two of the 
earlier known and largest have been suspected to possess 
an atmosphere, but this is doubtful. The effect of gravity 
on their surfaces must be very small indeed. Their only 
practical use in astronomy would be to determine the 
mass of Jupiter ; possibly that of Mars also ; and one of 
them (Yesta) has already been used for the former 
purpose. 

III. JUPITER. 

We now come to the most important planet, Jupiter, 
the largest in the solar system. In brilliancy, when in 
opposition, it rivals Venus ; and, though its apparent 
diameter varies between 50" and 30", it is always a very 
bright and conspicuous body. It revolves in an orbit 
but very slightly inclined to the ecliptic, and at a mean 
distance from the sun of 475,693,000 miles. The eccen- 
tricity of the orbit is moderate, -^ T6~3 j so that ^ s greatest 
distance from the sun can never exceed 500,000,000, 
nor its least fall short of 450,000,000 miles. The time 
taken in performing this extended orbit will of course be 
proportionally long, and is nearly twelve of our years. 
More accurately, Jupiter's year consists of 4,332*58 mean 
solar days. Its synodical period is 398*8 days; and its 
retrogradation, although it extends over a less arc than 
Mars', is performed much more slowly, requiring 121 
days. This is necessarily the case with each succeeding 
superior planet, in consequence of their greatly increasing 
distances. 

From the constant brilliancy of Jupiter, coupled with 
its great distance, it evidently follows, that-it must be a 



JUPITER. 



121 



very large and magnificent planet. Its apparent equa- 
torial diameter has been carefully measured, and is found 
to correspond to an actual length of 88,390 miles — that is 
to say, more than ten times the earth's, or than one-tenth 
of the sun's. A glance through a telescope shows that 
the planet is very considerably flattened, and the ellipti- 
city is usually set down as great as Y3TT' wn i° n gives a 
polar diameter of 81,940 miles only. 

The disc of Jupiter is usually crossed in a remarkable 
manner by dark-coloured belts, lying most generally in a 
direction parallel to the planet's equator. Sometimes 
only one or two are seen, frequently three, but occasion- 
ally the whole disc is covered with alternate belts of 
various intensities 
of shade. Jupiter 
is certainly sur- 
rounded by a dense 
cloudy atmosphere, 
capable of strongly 
reflecting the solar 
light. The dark 
belts are, in all pro- 
bility, rifts or 
fissures in the 
clouds, exposing the 
surface, and caused 
by violent per- 
manent winds, more 
or less resembling 
our own sub-tropical 
trade-winds. 

Besides these are 
spots, whose origin 




Fig. 34. 
occasionally seen small round bright 
is doubtful. They are not generally 
considered to be attached to the planet's surface, but more 
resemble bright patches of floating cloud. If we may 
hazard a conjecture, they are perhaps masses of cloud 
hanging about the summits of mountains, analogous to the 
ring-like craters of the moon ; and since spots similar to 
these, but dark, are also occasionally seen, these may 



122 ASTRONOMY. 

possibly be the craters themselves, free from the accom- 
panying vapour. It is by noting the passage of these 
across the disc that the time of Jupiter's rotation has been 
found. Notwithstanding its great size, the rotation is 
performed, without doubt, in so short a period as 9 h 55 1U 
21 -3 s of mean solar time. From this it follows that the 
centrifugal force generated at the equator of Jupiter must 
be very great, and the very considerable polar compres- 
sion is at once and satisfactorily accounted for. Indeed, 
Laplace has calculated what should be the ellipticity 
theoretically, as Newton did for the earth, and has found 
that it closely agrees with the amount observed. It 
would also appear that the rapid rotation produces the 
general parallelism of the belts. 

Jupiter is attended by four satellites, which form with 
their primary a very beautiful and complete miniature 
system. Its mass- has therefore never been a matter of 
doubt; and though various means have been employed 
in determining it, all have yielded almost identical results. 
The most accurate value is y/oTTsrir °^ ^ ne sun ' s mass; 
and it is thus the heaviest, as well as the largest planet 
in the system. The perturbations or disturbances which 
it effects upon the motions of comets and other bodies are, 
therefore, far more important than those of any other 
planet. 

From the particulars already given, it will be found 
that the bulk of Jupiter is 1,290 times the earth's bulk; 
its mass 300*7 times the earth's mass; and its density 
•233, or scarcely a quarter of the earth's average density, 
and 1-32 as compared with water. It will further be 
found that the force of gravity on the surface w 7 ill be 2*54 
times that upon the earth. 

The satellites of Jupiter, as seen from the earth, present 
most interesting, important, and varied phenomena. 
Their existence was first discovered by Galileo, and ever 
since they have occupied much of the attention of astrono- 
mers. They are distinguished from one another simply 
by numbers indicating their distance from Jupiter. It 
we imagine the planet to be represented by a globe three feet 



JUPITER. 123 

in diameter, the distances of the satellites from the centre 
of their primary will be very closely represented by 18, 
29, 46, and 81 feet respectively. As seen from the earth, 
they are of about equal brightness: the third, which is the 
largest, is generally rather more brilliant than the rest; 
and if it was not for the overwhelming light of the planet, 
they would probably just be visible to the unaided eye as 
very faint stars. As seen from Jupiter they will of course 
present phases like our own moon, and from certain 
periodical changes in their brilliancy, they are believed to 
resemble her also, in turning only one face to their 
primary; or, in other words, that, like her, they revolve on 
their axes in precisely the same time as they revolve in 
their orbits round the planet. These orbits are all circular, 
or very nearly so; and those of the two interior satellites 
do not deviate by the least appreciable amount from a 
strictly circular form; those of the two exterior are subject 
to slight variation. Their times of revolution round 
Jupiter are respectively 42^, 85^, 17 If , and 400J hours — 
so that they are far more swiftly moving bodies than our 
moon. Further, the orbits are all very slightly inclined 
either to the plane of Jupiter's orbit or to that of Jupiter's 
equator — a fact that considerably simplifies the theory of 
their motions. 

When we consider the great magnitude of Jupiter, and 
the positions of the orbits of his satellites, it is plain that 
the latter must be subject to very frequent eclipses. 
Indeed, the three interior moons pass through the shadow 
of the planet, and are eclipsed in every revolution; the 
fourth also is frequently eclipsed ; so that to the inhabi- 
tants of that distant planet such phenomena are of the 
most common occurrence. In like manner, they will pass 
between the sun and some point of the planet's surface j ust 
as frequently, and solar eclipses will be equally common, 
but of course are visible from only very small portions of 
the planet, owing to its immense distance from the central 
luminary. As seen from the earth, these phenomena are 
still further increased and varied. Not only do we see the 
satellites disappear on entering the shadow cone and 



124 ASTRONOMY. 

reappear on their emerging therefrom, as also the 
transit of a small black shadow across the bright planet, 
indicating a solar eclipse to all those portions over which 
it passes. We see further the frequent occultation of the 
moons as they pass behind the planet's disc and reappear 
on the other side, and we may observe the transit of 
the satellite itself projected on the disc, and accompanying 
at a greater or less distance its dark shadow, already 
spoken of. It will at once appear that when the planet 
is in opposition the shadow will fall directly below the 
satellite, and hence will not be seen, and the eclipses of 
the satellites will in like manner be invisible from the 
earth, owing to the planetary shadow cone lying directly 
behind the planet. Near opposition, also, the latter 
phenomena will only be partially visible, as the satel- 
lite may enter or emerge from the shadow cone, while 
it is hid behind the disc of the planet, according as 
Jupiter has past or not yet come into opposition with 
the sun. 

These continually changing phenomena are not only 
interesting but useful. The eclipse of a satellite forms an 
instantaneous signal of time visible over one-half of our 
earth, and thus it may be employed to compare the local 
times of two very remote stations. Or, if our tables are 
sufficiently perfected to predict the eclipse with accuracy, it 
may similarly be employed for determining the longitude 
at sea. This use of them was first pointed out by Galileo; 
and it explains why so much attention has always been 
paid to these bodies; bub, unfortunately, the difficulty of 
observing such delicate phenomena from the unsteady 
deck of a vessel almost precludes the use of this very 
promising method. 

The attempt to form tables which should accurately 
predict these occurrences, however, led Roemer to the very 
important discovery of the gradual propagation of light. 
His first predictions of the eclipses, which are the most 
important of the various phenomena, were founded upon 
the average of a large number of such observations made 
in every position of the planet with reference to the earth — 






VELOCITY OF LIGHT. 125 

that is, throughout the whole of its sy nodical revolution 
He soon detected, however, when he came to compare the 
predicted times with actual observation, that all those 
eclipses which happened near the time of opposition, 
Jupiter being then in perigee,* or nearest to the earth, 
occurred too soon; and, on the contrary, when Jupiter 
was in apogee, they occurred too late. The extreme vari- 
ation was very considerable, being about 16 m 26 s ; and 
it became evident to Roeroer that these irregularities 
would be at once explained, if the velocity of light was 
great, but not instantaneous, as it was previously supposed 
to be. In fact, if light required 16 m 26 s to travel 
across the orbit of the earth, by which amount the distances 
of Jupiter when at opposition and conjunction differ, the 
whole would be made clear. This solution of the difficulty 
was not generally accepted by astronomers till many years 
later, when Bradley discovered the aberration of light. 
It then became indisputable. 

The diameter of the earth's orbit being, it was supposed, 
about 190,000,000 miles, it followed that the velocity of 
light must be about 192,000 miles in a second. Later on 
still, experiments were made to measure the velocity 
directly when passing horizontally through atmospheric 
air on the earth's surface; and the result so nearly agreed 
with that derived from the observation of the satellites 
that no doubt existed upon the subject. These experi- 
ments have been repeated within the last twenty years 
with improved methods and apparatus; and the velocity 
determined is something less — namely, 184,000 miles per 
second. This was but a short time before the accepted 
value of the solar parallax began to be suspected; and 
it is most satisfactory to find that, since it has been 
necessary to reduce, the estimation of the sun's dis- 
tance, the two modes of measuring the velocity of light 
again agree most closely, thereby mutually confirming 
each other. 

* The term perigee is applied to any body, whether the sun or 
a planet, as well as to the moon, when it is at its nearest point to 
the earth. 



126 ASTRONOMY. 

The accompanying Table will give at a glance a general 
idea of the magnitudes and weights of the satellites : — 

Density com- Specific Gravity, 



Sat. 


Diameter 
in miles. 


Mass compared 
with the earth. 


pared with 
the earth. 


or the density," 

compared with 

water. 


I. 

11. 

III. 

IV. 


2,341 
2,101 
3,432 
2,936 


0-00521 
0-00699 
0-02661 
0-01283 


0-2016 
0-3738 
0-3267 
0-2515 


1-143 
2-120 
1-853 
1-426 



It will be seen that, excepting the third, they are not 
much larger than our own satellite, and that the two 
interior ones are of much less weight. The third satellite 
has twice the mass of our own moon, and the fourth is 
equal to it. As might be imagined, the matter of which 
they are composed is much lighter than that of the earth 
or her moon, but it is heavier than that of their own 
primary. This fact might readily enough be explained, if 
Jupiter is considered as a mass of heated matter, cooling 
slowly; but we must beware of too rash speculation upon 
what is only based on conjecture. Compared with the 
primary planet round which they revolve, the satellites of 
Jupiter are very small bodies indeed; and though the first 
is at a distance greater than the moon from us, it is very 
near when we consider the enormous magnitude of Jupiter; 
that is to say, while our satellite revolves at a distance of 
60 radii of her primary, the nearest of Jupiter's revolves 
at a distance of 6 radii only, and even its most distant at 
not more than 27 radii. One fact which renders the discus- 
sion of this miniature system of the highest interest is the 
confirmation which it affords of the laws of Kepler, which 
are observed to apply as accurately to the periods and dis- 
tances of the satellites as to those of the principal planets. 



IV. SATURN. 

This planet is the most distant of those known to the 
ancients. It is a tolerably conspicuous object, varying 
little in brilliancy or in apparent size, owing to its immense 
distance, compared with which that of the earth from the 



SATURN. 



127 



sun is but a small fraction. For the same reason it is 
very sluggish in its motion. Its mean distance from the 
sun is about 872,134,000 miles, and the eccentricity 
__i__ so that it may extend its excursions to a greater or 
less distance than this by about 50,000,000 miles. Nearly 
29^ years, or accurately 10,759*22 mean solar days, are re- 
quired by it to make the circuit of the sun. This slow 
motion allows the earth to come a second time between 
the planet and the sun in little more than a year; or, in 
other words, the synodical period is only 378 days; and 
though its arc of retrogradatiori is but 7°, it requires 139 
days to travel over this short space. 

The physical constitution of Saturn affords a striking 
exception to that of all the other planets. Not only is it 
accompaniecfrby no less than eight satellites of various sizes, 
revolving at very various distances (from 3~ to 64 radii of 




Fig. 35. 

Saturn), but it is surrounded by three circular, flat, con- 
centric rings, which revolve round the ball of the planet 
similarly to a very close satellite. The position of the rings 
with regard to the planet is most readily explained by a 
diagram (see fig. 35). These strange appendages render 
Saturn a most interesting object, although it is too distant 
for satisfactory observation of any markings on its surface 
beyond the identification of very faint belts, like those of 
Jupiter. The thinness of the rings is extreme, certainly 



128 ASTRONOMY. 

i 

not more than 250 miles, and in all probability very 
much less, but their diameter as well as their breadth is 
very considerable. The interior of the three is not con- 
spicuous, is even semi-transparent, and was not known to 
exist till the year 1850; but the two outer ones are very 
bright — indeed, are more strongly reflective of solar light 
than the ball of the planet. Extended series of angular 
measurements have been made to ascertain the various 
dimensions of this complex system. We shall append 
these particulars in a tabular form, but reduced to linear 
measure : — 

Equatorial diameter of Saturn, . . 71,903 miles. 

Polar diameter, 64,213 ,, 

Ellipticity, or Polar Compression, . -g-.-J^ ,, 

Extreme diameter of outer ring, . . 169,530 ,, 

Breadth of the outer ring, . . . 10,160 ,, 
Extreme diameter of middle or interior 

bright ring, 145,768 ,, 

Breadth of the middle ring, . . . 16,503 ,, 

Distance between these rings, . . 1,725 ,, 
Distance between the middle ring and 

the planet, 20,427 „ 

Saturn is thus even more elliptical than Jupiter, though 
its rotation on its axis is not quite so rapid. By watch- 
ing the passage of some darker regions on its surface it- 
is found to revolve in about 10 11 29 m ; and the rings 
have in a similar manner been observed to revolve 
in a period only 3 minutes greater. The rapid revolution 
of the rings tends greatly towards maintaining their 
equilibrium; for without it a very slight disturbance 
would be sufficient to precipitate them bodily upon the 
planet. Another fact which aids the conservation of this in- 
tricate and apparently unstable system is, that the rings are 
not quite concentric with the planet itself, revolving round 
a point about 450 miles distant from the centre of the ball. 
As seen from the planet, the rings and satellites must 
present a most gorgeous spectacle. To an observer on the 
illuminated side of the rings they will be seen to span the 
sky in broad arches of light, invariable in their position; 
with the satellites, various in size and phase, threading their 



SATURN. 129 

paths on either side. Upon the other half of the planet 
the rings will only be seen as black bands, occulting all the 
stars that lie in the direction, and causing a perpetuel 
eclipse of the sun over a portion of the hemisphere. 

The plane of the rings, which is probably coincident 
with that of the planet's equator, is inclined to the 
ecliptic at an angle of 28° IT; and since, like the earth, 
the planet revolves round the sun with the axis always 
parallel to itself, it is clear that, during half a revolution, 
or 14*7 years, the sun illuminates the northern, and for 
an equal time the southern side of the rings. Viewing 
them from the earth, which is comparatively near the 
sun, we usually see the illuminated side, whichever it 
may be, for the like periods. But when the sun is 
passing from the one side to the other, it is evident that 
it is only the thickness of the rings that is illuminated; 
and this is so extremely slight that, without the best in- 
strumental means, they are quite invisible at this time. 
Further, it is possible, during a short time, for the sun 
to be on one side of the plane of the ring and the earth 
upon the other. They will then, of course, be invisible 
from the earth, except as a dark band across the disc of 
the planet. The sun only passes once through the plane 
of the ring at intervals of 14*7 years; but the earth may 
pass three times at or near the time of the sun's passage, 
and on all these occasions the ring will be turned edge- 
wise towards the earth, and hence is invisible. 

It is then that the satellites, free from the glare of the 
rings, may be easiest seen, seven of them ranging along 
the line of the Saturnian equator, to which plane the 
eighth only is sensibly inclined. They are all small 
and faint, and two only are conspicuous enough to be seen 
in ordinary telescopes ; the whole system is far less 
interesting or valuable than Jupiter's, and have not been 
so much studied. One of them, Japetus, the most 
distant and second brightest, has been noticed to be 
always much fainter at one point of its orbit, and is 
therefore suspected, like Jupiter's moons, to rotate on its 
axis in a period equal to its revolution round its primary 
A I 



130 ASTRONOMY. 

Of what kind of matter the rings can possibly he com- 
posed has long been a disputed question. That they cannot 
be solid is certain, since it would be necessary, in order to 
preserve the equilibrium, that the parts near the planet 
should revolve much more rapidly than the more distant 
regions — a motion that would at once tear a solid to pieces. 
It is possible that they may be fluid; but there are reasons 
why even a fluid would be liable to fall upon the planet. 
The inner or " dusky " ring, from its semi-transparency, 
would seem to be composed of small solid bodies, each 
revolving in a separate orbit, and not so thickly strewn 
but that we are able to see through the interstices. It is 
also possible that the other brighter rings may be similar 
but denser streams of such small bodies. There may be 
portions where these are exceptionally dense and numerous, 
which would explain the variability of brightness of differ- 
ent parts, and the existence of such denser portions would 
likewise tend greatly towards the stability of the System. 
The total mass of the rings has been found to be about T ^ 
the planet's mass. 

The mass of Saturn itself has been found by various 
methods, particularly from the observation of the sixth 
and largest satellite (Titan). The accepted value is 
tt-^tt-.tt of the sun's, from which it will be found, on com- 

o > o O 1 o I ' 

parison with the dimensions of the planet already given, 
that the matter of Saturn must be very light indeed, 
having but -1334 of the density of the earth, or -756 of 
water. The average component matter of Saturn would 
thus readily float upon water, not being heavier than 
ordinary deal. Of the satellites we know very little, and 
even the diameter of the largest is open to question. 
They are, however, certainly smaller than Jupiter's, and 
are probably similar in density to their primary 



V. URANUS. 

While examining some stars in the constellation of 
Gemini, on the evening of March 13, 1781, the elder 
Herschel noticed one which appeared to have a disc. 



URANUS. 131 

Tins he first thought to be a comet; but when sufficient 
observations of it had been made, it was found to be a 
planet revolving round the sun exterior to Saturn, at a 
mean distance of 1,753,850,000 miles, in a period of 
30,686*7 days, or more than 84 years. It will readily 
be understood that this object is too distant for satis- 
factory examination. It presents to us a very small disc, 
of uniform brightness, about 4" in diameter, and shines as 
a star of the sixth or seventh magnitude. It is therefore 
barely visible to . the naked eye when most iavourably 
situated, and is fainter than the minute asteroids, Yesta 
and Ceres. Its real diameter will be about 33,023 miles. 

Uranus is attended certainly by four satellites. They 
are extremely faint objects, but they are interesting, as 
forming an anomaly in the solar system. It is to be 
remarked that all the planets revolve round the sun in 
orbits but little inclined to the ecliptic. Moreover, all 
motion, whether that of the planets round the sun or 
that of rotation on their own axes, is invariably performed 
in one direction — viz., from west to east. The satellites of 
the Earth, Jupiter, and Saturn conform to the same 
characteristics; but when we come to Uranus, we find 
that its moons revolve in the opposite direction, or from 
east to west, and further, that the plane of their orbits is 
inclined to the ecliptic at an angle of 78° 38', or not far 
from perpendicular to it. They are thus the sole, but a 
very remarkable exception to what seems to be a general 
law of planetary motion. If, as we are led to conclude 
from analogy, the planet's equator lies nearly in the 
plane of the orbits of the moons, the axis of rotation of 
Uranus must lie very nearly in the plane of its own 
orbit. This would produce the strange effect of bringing 
the sun vertically over every part of its surface in the 
course of a revolution. No rotation on an axis has been 
observed, nor has any spheroidicity been noted with 
certainty, but the unusual position of the planet's axis 
offers obstacles to the identification of this fact. 

The mass of Uranus has been calculated in various 
ways; the best estimation is probably -5-4, tot of the sun's, 



132 ASTRONOMY. 

Assuming the diameter given aoove to be correct, and the 
planet to be spherical, we shall find the density of the 
planet to be 0-174 as compared with the earth, or 0*99 as 
compared with water. It is therefore slightly heavier 
than Saturn. It is noteworthy, that the distance of 
Uranus is so great that the light and heat of the sun will 
be only -^g- part of the intensity on the earth, and that 
the apparent diameter of the sun as seen from it, will be 
but -^ of its diameter as seen by us — facts that must have 
immense influence on the planetary economy. 

The eccentricitv of the orbit of Uranus is verv nearly 
the same as Jupiter's, gi.la ^ ^ut tne exac ^ determination 
of the elements of its orbit was long a perplexing question, 
for reasons that will be stated in the ensuing section. 

VI. NEPTUNE. 

A brief consideration of the law of gravitation will 
lead us to the conclusion that the motion of a planet can 
never be a strict ellipse round the sun. Every object in 
the solar system tends to draw it away from its true path 
with ever- varying force and direction. If it was not that 
the forces the planets exert upon each other are very 
small, owing to their great distances from one another, 
and the great preponderance of weight or attractive power 
resident in the sun, their motions would be intolerably 
complicated, and in all probability would have been for 
ever inexplicable. Fortunately, the effects of planetary 
perturbations are only very slight disturbances, discernible 
by the most careful observation. Still, it will be readily 
understood that the effects of the gravitation of a planet 
upon the one next it will be sensible, especially if the 
disturbing body is large, and particularly when the dis- 
turbing and disturbed body are in conjunction or have 
the same longitude, as seen from the sun* — in other words, 

* It is often necessary to reckon longitudes and latitudes as 
seen from the sun ; they are then called heliocentric. If the centre 
of the sun be taken as the origin of co-ordinates, and the ecliptic 
as the plane of reference, heliocentric latitude will be the angular 



NEPTUNE 133 

when they are at the least possible distance from one 
another. 

When Uranus had been observed for some years, care- 
ful calculations of its orbit were made, and its path traced 
out iu advance with all possible accuracy, the disturbances 
produced by Saturn and Jupiter being rigorously taken 
into account. Yet it was soon found to deviate consider- 
ably from its predicted orbit, and suspicions arose as to 
the possible existence of an ultra- Uranian planet which 
was causing the deviation. The problem that was then, 
presented to astronomers was to point to the position of 
a disturbing planet, which should be capable of producing 
the effects on Uranus which had been observed. This 
was attempted almost simultaneously by two astronomers, 
Adams in England, and Le Verrier in France; and not- 
withstanding the enormous difficulty and novelty of the 
problem, they each arrived independently, and by different 
methods, at results in close agreement with one another. 
A search was then instituted near the place indicated, 
and it was crowned with success by the discovery of the 
planet, since called Neptune, very near indeed the pre- 
dicted place, by Dr. G-alle, upon September 23, 1846. 
This is one of the most brilliant triumphs of astronomical 
science, and reflects the greatest credit upon the eminent 
geometers who brought it to so successful a termination. 

From the time of the discovery of Uranus (1781) until 
the year 1822, when the two planets were in conjunction, 
Neptune had been increasing the velocity of Uranus, and 
after that date it had been retarding its motion. During 

distance of a body north or south of the ecliptic, and heliocentric 
longitude the angular distance measured on the ecliptic from the 
first point of Aries. The advantage of this system of co-ordinates 
is, that the sun being fixed, at least with reference to the planets, 
any change in the latitude or longitude is the effect of an absolute 
change of direction of the object; whereas, in any change of geo- 
centric latitude and longitude, the absolute movement is neces- 
sarily mixed up with the motion of the earth itself. It will be 
understood that the sun's geocentric latitude being always nothing, 
the earth's heliocentric latitude will also be nothing ; and the sun's 
geocentric longitude will be the same as the earth's heliocentric 
longitude, plus 180°. 



134 ASTRONOMY. 

the greater part of the interval it had been drawing 
Uranus slightly from the sun, with a force which reached 
its maximum at the conjunction in 1822. 

The orbit described by this planet requires no less than 
164|- years for its completion, and the mean distance from 
the sun is 2,746,250,000 miles. Its eccentricity is small, 
__i T . T only. It shines like a star of the eighth magnitude, 
and has a minute but measurable disc, from which its 
real diameter has been found to be 38,180 miles; but 
such delicate measurements are liable to very sensible 
error. Neptune possesses one minute satellite, and pos- 
sibly another; so that its mass is better known than 
might be anticipated. It is equal to xf.Vso" °^ ^ ne suns 
mass. This gives a density of T50 compared with the 
earth, or *848 compared with water. The sun will shine 
with only -^^ part of its intensity on the earth, and but 
^",^30" part of its intensity on Mercury. 



QUESTIONS. 

1. To what variations in brilliancy, apparent diameter, and 
distance from the earth is Mars subject? 

2. Give the mean distance of Mars from the sun, and its 
diameter in miles. 

3. What are the sidereal and synodical periods of Mars ? In 
what part of the latter do superior planets retrograde ? 

4. To what phase is Mars subject, and whence does it arise ? 

5. What is the mass and density of Mars ? 

•3 State what is known of the climate of Mars. Compare thd 
seasons upon the Earth and upon Mars. 

7. Give the time of rotation and the amount of polar com- 
pression. 

8. Describe the general appearance of this planet. Whence 
does the redness of its light arise ? 

9. Compare the intensities of solar light and heat on Mars and 
the earth. 

10. Give the history of the discovery of the asteroids. What is 
OPoers' hypothesis ? What is known of their collective mass and 
probable numbers? 

11. State what is known or conjectured of the magnitude and 
brightness of the asteroids. 

12. Summarize the points of difference between the major and 
minor planets. 



QUESTIONS. 135 

13. Give the extreme limits of the zone of small planets, and the 
periods of the nearest and most distant of them. 

14. State the period and distance of Jupiter; also, its synodical 
period. 

15. What are the limits of the apparent diameter of Jupiter; 
likewise its real diameter in miles, and the polar compression ? 

16. Describe its general appearance, and explain the nature of 
its belts. 

17. What is the time of Jupiter's rotation? How has it been 
found? 

18. Give the mass of Jupiter compared with the sun; also, its 
volume, mass, and density compared with the earth. 

19. State the number and relative distances of Jupiter's moons. 
In what particulars do they resemble our own ? 

20. State their respective times of revolution round Jupiter. 

21. From whence arises the frequent eclipses of the satellites ? 

22. Explain the various phenomena of the moons as seen from 
the earth, and how are they modified when Jupiter is in oppo- 
sition ? 

23. To what use have the eclipses been applied ? With what 
success ? 

24. How did the observations of the eclipses lead to the dis- 
covery of the velocity of light ? 

25. What is the most recent evaluation of the velocity of 
light? 

26. Compare the dimensions of Jupiter's moons with our own, 
and with their primary. 

27. What is the mean distance and period of Saturn? and 
give an illustration of its slow motion. 

28. How many and at what distances are the satellites of 
Saturn ? 

29. How many and of what nature are its rings ? 

30. What are the dimensions of this planet ? and give a general 
idea of the size and thickness of the rings. 

31. State the time of rotation of Saturn and its ellipticity. 

32. What causes contribute to the stability of the rings ? 

33. Describe the appearance of the rings to an observer on 
Saturn. 

34. Under what conditions are they usually seen from the 
earth? Explain why the opposite sides are alternately illumi- 
nated, and for what time. 

35. State a peculiarity in the light of Japetus, and the conclu- 
sion drawn from it. 

36. Discuss the question of the constitution of the rings. Com- 
pare their collective weight with that of Saturn. 

37. How has the mass of Saturn been found? What is the 
result? Give its density. 

38. By whom and when was Uranus discovered? 



136 ASTRONOMY. 

39. State its distance and period ; also, its brilliancy, real and 
apparent magnitude. 

40. What peculiarity is observed in the motion of its satellites ? 

41. If this peculiarity extends to the planet's rotation, what 
would result? 

42. What is the mass and density of Uranus? What the in- 
tensity of solar light and heat there ? 

43. Explain the terms heliocentric longitude and latitude. 
What is the advantage of these co-ordinates ? 

44. Why are planetary perturbations always small? Under 
what circumstances are they greatest ? 

45. Whence arose the difficulty of accounting for the motions of 
Uranus ? 

46. Give the history of the discovery of JSeptune. 

47. What is its period and mean distance ? Likewise, its mil 
diameter and mass ? How has the mass been found ? 

48. Contrast the intensity of light and heat on Keptune with 
its intensity on the Earth and Mercury. 



137 



CHAPTER VII. 

I. COMETS. 

Throughout all ages comets have excited tlie most pro- 
found interest, in consequence of their strange and erratic 
character. Their sudden appearance, their surpassing 
brilliancy, and their astounding apparent size has ever 
made them objects alike of dread and of admiration, and 
has ensured the record of their appearances in all old 
chronicles. We are thus made acquainted with the 
apparition of some hundreds of comets, many of them at 
periods very remote. Still it is certain that a far greater 
number has escaped without being seen. But few are 
now found to be visible to the naked eye, compared with 
those visible only by the aid of the telescope, of which 
five or six are frequently found each year. Large num- 
bers also must be invisible, in consequence of their orbits 
lying in such a manner as only to be above the horizon in 
the daytime. Thus, for instance, one large comet was 
seen (a.d. 62) during the rare conjunction of a total 
eclipse of the sun. This fact is recorded by Seneca; and 
the comet would unquestionably have escaped but for 
this unusual coincidence. It will appear, therefore, that 
the number of comets that belong to the solar system 
must be very large, probably many thousands. 

Although assuming an immense variety of forms, comets 
generally consist of three distinct parts — the nucleus, the 
coma, and the tail; but not infrequently one or even two 
of these parts are wanting. The nucleus is a small bright 
point or disc, situated in the densest part or head of the 
comet, and sometimes assuming the minute, sharp, and 
dazzling appearance of a star. This is the solid part of 
the comet, if indeed any is really so dense, and it is 
evidently the part upon which the other developments 
depend. The coma is a nebulous haze surrouuding the 



138 ASTRONOMY. 

nucleus like an envelope of atmosphere, usually semi- 
circular in the direction of the comet's }3ath, but frequently 
fading imperceptibly into the third and most remarkable 
part of the comet — its tail. This latter is usually a hollow 
conical appendage, stretching often to immense distances, 
and generally in a direction opposite to the sun. Comets 
are, however, frequently observed having no tails, and 
sometimes with more than one, directed in different ways. 
Frequently the nucleus is wanting, and the comet pre- 
sents nothing more than a circular or oval, faint, hazy 
disc. 

It is in the latter form that they are usually first 
descried, and while approaching and passing round the 
sun the various phenomena and developments occur. As 
it nears the sun the disc is observed to contract, and 
eventually a condensed and brighter part is seen to form 
at or near the centre of the coma, forming gradually a 
nucleus, the whole slowly increasing in brightness. When 
still nearer, a bright jet as of gas is projected from the 
nucleus in the direction of the sun, which, after proceeding 
a short distance, is gracefully curved round and thrown 
back in the opposite direction, forming a tail often of 
enormous length. This is generally brighter at the edges 
than in the centre, giving it the precise appearance of a 
hollow cone, to which the coma forms a hemispherical top* 
The form and direction of the jets are very various, not 
only in different comets, but in the same comet at differ- 
ent times, and their continuance is apparently capricious. 
But the rapidity with which a taii is formed by them, and 
the immense distances to which it extends, plainly indi- 
cates the most violent commotion going on in the nucleus 
of the comet. Most commonly these marvellous changes 
reach a maximum, and the comet assumes its most splendid 
appearance shortly after it has passed its perihelion, point- 
ing thus to the sun as the exciting cause ; but sometimes 
the tail has disappeared before the perihelion is arrived 
at. As the comet leaves the sun it usually goes through 
similar changes in the opposite order, and appears to 
absorb again the matter it has emitted, and to return to 



COMETS. 139 

the condition in which it was when first seen. Such are 
the phenomena generally witnessed, but there are many 
exceptions to the rule, and scarcely two comets can be 
found that present precisely the same features. 

When we come to inquire what is the physical consti- 
tution of comets, we are at once involved in difficulty. 
They are certainly bodies of very little weight or mass, as 
is proved by the fact that in 1779 a comet passed through 
the orbits of Jupiter's moons without in the least derang- 
ing those bodies. Another comet has twice passed very 
near to Mercury, but without causing any change in its 
orbit. It is also certain that the matter of which 
the coma and tail, and possibly in some cases even the 
nucleus, are formed, must be of the most extreme tenuity. 
Faint stars have frequently been passed over, not only by 
the tails, but by the most dense parts of a comet without 
any diminution of their brightness; and as such stars 
would have been totally obscured by a slight fog on the 
earth's surface only a few yards thick, it follows that the 
vapour of a comet must be of extreme rarity as compared 
with such a fog. Refraction through the vapour of a 
comet should cause a displacement in the position of stars, 
supposing it to have any conceivable density, but no such 
displacement has been observed. It would therefore seem 
that, notwithstanding the enormous dimensions of the 
tails of comets, they will not weigh more than a few 
pounds, or possibly ounces. Newton has calculated that a 
globe of atmospheric air one inch in diameter, carried to 
an altitude from the earth equal to its radius, would 
expand itself through all the planetary regions as far as 
the orbit of Saturn. It is not surprising, therefore, that 
the atmosphere or gas suiTOunding a body of so slight a 
mass as a comet should thus diffuse itself, though it is still 
impossible to account for the fact that the tail appears 
to be subject to a strong repellant force appertaining to 
the sun. 

There remain, however, many strange phenomena con- 
nected with this subject in need of explanation. The 
matter of which the tail is composed is occasionally, in the 



140 ASTHOKOMY. 

case of comets that approach the sun very nearly, whirled 
round, entire, through many millions of miles in the space 
of a few hours, retaining always a direction opposite to 
the sun, in apparent defiance of all law ; and it further 
seems almost inconceivable that the matter thus emitted 
can be collected again by the feeble attraction of a comet. 

Notwithstanding their small weight and extreme tenuity, 
they are capable of shining with great brilliancy. Several 
have been visible in the day time, and some even in close 
proximity to the sun — as, for example, the great comet of 
1843. On the other hand, some are so faint and ill- 
defined as to be amongst the most difficult objects to ob- 
serve. They shine, unquestionably, by reflecting solar 
light — a fact satisfactorily proved by Arago with the aid 
of his polariscope. This is an instrument devised to dis- 
tinguish between direct and reflected or polarized light, 
and which depends upon the different course taken by 
these rays in passing through any doubly-refracting 
crystal, as Iceland spar. But it is also certain that they 
shine by their own proper direct light — facts not incom 
patible. This has been shown by the spectroscope, an 
instrument that has given us a most astonishing insight 
into the nature of light and the constitution of the 
heavenly bodies, but to which it is only possible to allude 
in the present work. Attempts have frequently been 
made to prove the existence of phases in comets, but 
without success. When it is remembered that they are 
not solid bodies, but are more of the nature of a cloud or 
smoke, capable of reflecting light among their own 
particles, phases will be understood to be impossible. 
The nuclei of some are probably solid, and must exhibit 
phases, but they are too small to be satisfactorily made 
out. 

To the earlier astronomers the motions of comets were 
a complete puzzle. The merit of first determining the 
form of their orbits belongs to Newton. He demonstrated 
that any curve of the conic sections was compatible with 
the law of gravitation, and pointed out that the orbits of 
comets would be in the form of an ellipse of great eccen- 



COMETS. 141 

tricity or of a parabola, which is the limiting form of the 
ellipse — i.e., one whose eccentricity is infinity. The orbit 
of the comet of 1680, one of the most remarkable of any, 
was calculated by him, and fully confirmed the views he had 
expressed only five years before in the Principia. Comets 
are visible only during a short period, when they are 
passing perihelion, by far the larger part of their extended 
orbits being performed at distances too remote for them 
to be seen by us. The orbits of the great majority differ 
very little, if at all, from a parabolic form during the 
time that they are visible. This implies either that they 
will not return to the sun, or that the distances to which 
their elliptical orbits extend is so enormous that they 
require the lapse of ages to perform their revolutions. A 
few have been ascertained w 7 ith certainty to move in 
hyperbolic orbits; but generally these differ so little from 
the parabola as to lead to the suspicion that they have 
originally had that form, and that the attraction of some 
planet has so quickened their motion as to give it the 
form of the hyperbola.* These, of course, can never 
return to the sun after having once passed perihelion, but 
must travel on to other systems, or be lost in the im- 
mensity of space. The remainder move in orbits of 
moderate eccentricity. 

The inclination of the orbits of comets to the ecliptic is 
often very great, and in some instances is nearly perpen- 
dicular to that plane; their motion also is as frequently 
retrograde as direct — facts which contrast strongly with 
planetary characteristics. It has, however, been noted 
that the comets of short period (seven in number) conform 
to the planetary rule — namely, direct motion and small 
inclination to the ecliptic. 

The distances of the cometary perihelia from the sun is 
various, but never very great. The majority approach 

* It is to be remarked that the velocity of motion in the para- 
bola is greater than in the ellipse, and in the hyperbola greater 
than in the parabola, the distances from the sun being supposed 
equal. This explains, therefore, how a comet can approach the 
sun so nearly, and yet be able to disentangle itself again from the 
powerful attraction of that body. 



142 ASTRONOMY. 

the sun nearer than the earth's mean distance, and all 
are included within the orbits of the asteroids: Some, 
however, and these principally the larger and brighter 
comets, pass extremely near the sun. The great comets 
of 1680 and 1843 are most remarkable in this respect. 
The latter approached the sun's surface within 80,000 
miles, or less than 4 of the solar radius, and the former to 
within ^, or 142,000 miles. For a time, therefore, they 
must have been subjected to a most intense heat — which 
may possibly account to some extent for the changes which 
they underwent, as well as for the enormous distance to 
which their tails extended. The tail of the comet of 1843 
had an apparent length of not less than 65°, and its actual 
length must have been more than twice the earth's dis- 
tance from the sun; and that of the comet of 1680 must 
likewise have exceeded the same unit of measurement. 
It has been calculated by Sir J. Herschel that the heat 
sustained by the former of these comets was equal to 
47,000 times that of the sun at the distance of the earth — 
a temperature more than sufficient to melt cornelian, agate, 
or rock crystal ! How it is possible for these flimsy bodies 
to sustain this glare, and yet emerge from it none the 
worse for the exposure, is one of the singular enigmas 
connected with this subject. 

It is to be noted, however, that the intense heat is to 
some extent compensated by the short time of exposure. 
This comet was travelling at the rate of 366 miles per 
second at the time, and in the space of an hour from the 
perihelion passage, would have escaped to a distance 
where the glare would be but \ of that mentioned. 
Neither is it, perhaps, quite correct to say that they ex- 
perience no loss from the intense heat, and the changes to 
which it gives rise. It has been observed that in the 
case of those comets which return frequently at short 
intervals, that they appear less bright at each succeeding 
apparition — pointing to a waste of material from some 
cause or other. 

The aphelion distances of those comets that move in 
elliptical orbits is often very great, extending far beyond 



COMETS. 143 

the orbit of Neptune. Thus the great comet of 1811, one 
of the most brilliant of the present century, and the length 
of whose period exceeds 3,000 years, extends to fourteen 
times the distance of Neptune, or 38,493,000,000 miles. 
There is good reason to believe that some, retreating to a 
much greater distance, may return after the lapse of several 
thousands of years; but since they are only visible at most 
for a few months, the elements are to some extent un- 
certain, and a parabolic orbit would equally well satisfy 
their movements during the short period of their visibility. 
It is natural that more interest should be attached 
to those comets whose periods are comparatively short, 
although they may be much less splendid objects. Of 
these the comet of Halley is the first in importance. It 
was the first whose return was predicted, and which 
actually came into perihelion at the calculated time. Its 
orbit was computed by Halley from its apparition in 1682; 
and from the similarity of its elements with those of other 
cometary orbits, which he had computed as belonging to 
comets that appeared in 1378, 1456, 1531, and 1607, he 
was led to conclude them to be identical. Attributing to it 
a period of 76 years, he ventured to predict its reappearance 
in 1759. This comet is frequently retarded by the attrac- 
tion of the planets, especially Jupiter, and this causes the 
intervals of its appearance to be rather irregular; but no 
doubt can exist as to the identity of the comet as seen at 
the above mentioned dates. It has now twice returned to 
perihelion — in 1759, when its coming was looked for with 
the greatest interest, and in 1835. In the first instance it 
arrived at perihelion within a month of the computed 
time, and in the second, its orbit being better known, 
within five days, all the perturbative effects of the planets 
having been carefully taken into account. The mean 
distance of Halley's comet from the sun is scarcely so great 
as that of Uranus, and its aphelion distance is beyond, but 
not greatly beyond, the orbit of the planet Neptune 
(3,235,500,000 miles). Several other comets are now 
known to have orbits similar to this, and together form a 
group of themselves, possibly having a common origin. 



144 ASTRONOMY. 

Perhaps even still more interesting is the second family 
or group of comets of short period, which revolve in orbits 
for the most part interior to that of Jupiter. Seven 
members are at present known, having periods varying 
from 3^- to 7J years. The first (Encke's) has made twenty- 
six revolutions since its first discovery by Pons, in 1786, 
and has been observed at eighteen separate apparitions, 
upon each occasion forming the theme of the most careful 
discussions. These have brought to light the important 
fact, that its period is slowly diminishing at the rate of 
about 2^ hours each revolution. It follows that the dis- 
tance from the sun is slowly diminishing, and the con- 
clusion would naturally be 7 that eventually, in the lapse 
of ages, the comet must fall into the sun, if not previously 
dissipated by its heat. Whether any circumstances will 
avert such a catastrophe is at present quite unknown. 

This peculiarity has led to speculations as to its probable 
cause; and the suggestion of Encke, that there may exist 
in the inter-planetary space an ethereal medium so rare 
as not to affect the motions of solid bodies as the planets, 
but capable of producing a retardation of velocity in 
comets, has generally been received with favour. The 
effect of such retardation would evidently be to allow 
the comet to be drawn nearer the sun, and hence to 
shorten its period. The resisting medium is the name 
applied to this supposititious ether; but it is quite 
possible that other causes may be found adequate to 
account for the observed fact without having recourse to 
conjectures of this nature. It is nevertheless considered 
by many astronomers to have a real existence, and to be 
the true explanation of the shortening of the period of 
this comet. 

Another most interesting member of this group is the 
comet known as Biela's, which was first seen in 1772, and 
which has a period of about 6J years. From the time of 
its discovery till 1852, when it was last seen, it had made 
twelve revolutions and been visible six times. From some 
unknown cause the comet has never been found since the 
latter date. What renders this comet so extremely in- 



COMETS. 145 

teresting is the fact that, during the apparition, in 1846, 
it was observed to divide into two comets, which attained 
nearly equal lustre, and which travelled side by side in 
separate orbits, maintaining a constant distance from each 
other. At the next return, in 1852, both members were 
found still travelling in company, but separated by a 
rather greater interval. The possibility of such an 
extraordinary circumstance renders the solution of the 
vexed question of the physical constitution of • comets 
still more difficult; but it may perhaps aid us in under- 
standing how groups of comets come to exist having 
similar periods. 

Of late years, the most splendid comets have been those 
of 1858 (Donati's) and 1861. The first was remarkable 
for the brightness of its nucleus, and the marked and 
graceful curve of its tail. This last is a frequent feature 
in comets, and is caused by the change of the velocity, 
since the matter of the tail had been emitted from the 
nucleus. This was certainly one of the long period 
comets, requiring more than 2,000 years for one revolu- 
tion in its elliptical orbit. The comet of 1861 was noted 
for the great apparent length of its tail (105°), and for 
the unusual circumstance that the earth passed either 
through or very near the tail, upon the evening of its 
first discovery, in the northern hemisphere (June 30, 
1861). 

The most important discovery of modern times, relating 
to the theory of comets, is their unexpected and rather 
mysterious connection with the streams of meteors through 
which the earth occasionally passes. The most important 
of these streams is that which gives rise to the well- 
known shower of November meteors. Upon almost any 
clear night one or two shooting stars may be seen by a 
patient observer, but upon certain nights of the year 
these are much more numerous. Kecords are not wanting 
of very remarkable showers occurring at different dates, 
the earliest being October 13, 902 O. S., and it has been 
found that similar extraordinary showers have happened at 
regular intervals of thirty-three years, though the day of 
A. K 



146 ASTRONOMY. 

their occurrence advances slowly on the calendar, so as to be 
equivalent to November 13, N. S. in the present century. 
The shower is an annual one, but at the intervals stated 
it assumes a much more imposing character than ordinarily. 
The explanation of these phenomena is, that there exists 
an annulus of meteors, or minute planets, revolving round 
the sun in a long ellipse, and in a retrograde direction, in 
a period of thirty-three and a quarter years, and that 
there is one point of the ring where it has a much 
more considerable density — i.e., where the meteors are 
more closely packed, than elsewhere. The perihelion 
of their orbit lies very near the earth's orbit, and 
that planet meets them and passes through the ring 
each year, encountering the densest part of it only once 
in thirty-three years. Of course, the gravitation of the 
earth attracts the nearest of the group so powerfully as 
to cause them to fall to the earth, if their extinction is not 
previously occasioned by the heat evolved in their passage 
through the atmosphere, which will invariably be the 
case of all the smaller ones.* 

It has been observed further, that the meteors of any 
night radiate always from some particular point of the 
heavens — those of November from that point towards 
which the earth is moving at the moment, yet not precisely 
so, for the radiant point is not on the ecliptic, but con- 
siderably to the north of it. From the amount of the 
deviation it is possible to compute the inclination of the 
meteoric orbit to the ecliptic. The perihelion distance of 
the orbit and the longitude of the node are of course none 
other than the distance of the earth from the sun, and its 
longitude at the moment that it encounters the densest 
part of the stream. In this way the elements of the 
meteoric orbit have been approximately arrived at, when 
it was soon discovered that they precisely agreed with 
those of a comet of like period, known as Tempel's comet, 

* Specimens of those that have actually fallen are common in 
museums, and have frequently been chemically analyzed. Some 
are very small; one, however, is known to exist on the plains of 
South America too heavy for transportation. 



QUESTIONS. 147 

and which had been visible in the year 1866. We are 
thus obliged to ascribe a community of origin to these 
bodies and the comet ; but of what precise nature is the 
connection is at present unknown. 

A similar discussion has led to the identification of the 
orbit of another well-known meteoric stream (that causing 
the annual shower of August 10) with that of a comet 
observed in 1862. Many other streams of meteors are 
known to exist, giving rise to annual showers, but of far 
less imposing character, and each of these have their 
proper radiant point \ but they have not yet been identi- 
fied with the paths of any known comet. This branch of 
astronomy is extremely interesting and of growing im- 
portance, but we may not refer to it at greater length 
here. Very much yet remains to be added to our know- 
ledge of meteors, aerolites, &c, and their connection with 
comets. 

QUESTIONS. 

1. Give reasons for believing the number of comets to be very 
great. 

2. Describe the several parts of a comet. Give their designa- 
tions. Are they found in every comet ? 

3. Describe the general appearance of a comet when first 
descried. Trace the changes it undergoes during its apparition. 

4. What is the usual direction of comet ary tails? Describe the 
phenomena of their development. 

5. What is the probable cause of the changes comets undergo? 
Upon what part do they principally depend ? 

6. Prove that the mass of a comet is usually insignificant. 

7. Prove that the materials composing them is of extreme 
rarity. 

8. Enumerate some of the difficulties to be explained in the 
phenomena of the tails. 

9. Give an illustration of the brightness of comets. 

10. How do we know that they shine by their own proper light, 
and also by reflecting solar light ? 

11. Should comets present phases? Why have none been 
observed ? 

12. Give the possible forms of cometary orbits and an idea of 
their relative frequency. 

13. Compare the relative velocities in each of the three forms. 

14. Contrast the inclinations of cometary and planetary orbits. 
Give one marked case of similarity. 



148 ASTRONOMY. 

15. State the limits of the distances of comets from the sun in 
perihelion. Give instances of very near approach. 

16. Estimate the amount of heat sustained by the great comet 
of 1843. What effect had it upon the comet? How long en- 
dured? 

17. Do comets suffer loss from exposure to the solar heat ? 

18. Give illustrations of the aphelion distances of elliptical 
cometary orbits. What is that of Halley's comet ? 

19. How was the period of Halley's comet established ? How 
nearly to computed time has it returned to perihelion ? Why are 
the intervals irregular ? 

20. How many comets of short period are known ? What are 
their periods, and within what limit are they for the most part 
confined. 

21. State a peculiarity of Encke's comet, and what must result 
from it ? 

22. How is the shortening of its period explained ? 

23. State a peculiarity of Bielas comet. 

24. What were the remarkable characteristics of the comets of 
1858 and 1861 ? 

25. Explain the cause of the annual appearance of the November 
meteors, and also of the extraordinary displays that occur at 
intervals. 

26. What is the period of their orbits and the date of the first 
recorded extraordinary display? 

27. What is meant by the radiant point ? How has the orbit of 
the meteors been determined ? 

28. With what cometary orbit is the meteor stream coincident? 
Have similar coincidences been found iu any other cases ? 



149 
CHAPTER VIII. 

PERTURBATIONS. 

To treat fully of this interesting but complicated branch 
of astronomy would be far beyond the range of the present 
work; but it is nevertheless the case that some classes of 
perturbation are far too important to leave untouched. 
Of these the precession of the equinoxes, nutation of the 
earth's axis, and the tides, are examples. The latter, being 
of the greatest terrestrial moment, will be treated first. 
A brief sketch of lunar and planetary perturbation will 
also be appended, that the student may form some notion 
of their nature ; but to trace their causes would in most 
cases require a higher knowledge of mathematical reason- 
ing than is here assumed. 

I. THE TIDES. 

A very superficial observation of the tides shows them 
to depend chiefly on the moon, and this has long been 
known. The explanation of the manner in which they 
do so was first given by Newton. The moon's attraction 
upon the earth, considered as a rigid, solid body, acts upon 
its centre; but the waters of the ocean vertically below 
the moon experience and obey a greater attraction, being 
nearer. An immense flat wave is thus heaped up below 
the moon. On the other hand, the moon's attraction on 
the rigid earth being greater than on the waters upon the 
other side of the globe, a similar wave is left heaped up 
there also. It is thus the difference of the moon's attrac- 
tion upon the waters on opposite sides of the globe 
vertically below her that causes the two tidal waves. 
Secondly, the earth being in rotation, and the moon's 
attraction always keeping these waves below her, they will 
clearly traverse the earth, following the diurnal motion of 



150 ASTRONOMY. 

the moon. The intervals of the arrival of the lunar tidal 
wave at any place is therefore half the apparent lunar day, 
or, upon an average, 12 h 24 m . 

It is evident further that the sun will have a precisely 
similar wave below it, which, in consequence of its great 
mass, is of considerable height. It is inferior to the 
moon's, because its much greater distance renders the 
diiference of its attraction on either side of the earth but 
slight. The proportion is as 25 to 10, or, since the lunar 
wave in the open sea is 2^ feet in height, the solar will be 
one foot only. The period of the solar tidal wave will be 
half a solar day, or about twelve hours. In consequence, 
however, of the friction met with, neither wave exactly 
follows the attracting body, and does not arrive, even at 
places where the land does not further delay it, till about 
three hours later than the meridian passage of the sun or 
moon. 

It will be observed that the solar wave always gains on 
the lunar, and that their superposition is inevitable. This 
of course takes place when the moon is in syzygy, when 
there will be but two waves, the sum of the effects of both 
sun and moon. This is called the spring tide. At all 
other times there will be four tidal waves of unequal 
height. Practically, however, this is not the case, for a 
blending of the solar and lunar waves must take place. 
"When the moon is in quadrature (90° distant from the 
sun), this will be effected by a reduction of the height of 
high water and a raising of the level of low water. The 
solar wave will be coincident with the lunar low tide, 
and will therefore raise it; and the lunar wave alone, tend- 
ing to produce high water, it will be less than ordinary. 
These are called neap tides, and the range will evidently 
be small compared with the spring tides. 

Another peculiar effect of this blending will be felt on 
either side of the syzygies. It being remembered that 
the time of high water does not depend upon the arrival 
of the solar or lunar wave, but upon the effective height 
produced by their combination, it will be apparent that 
before the new or full moon, high water will occur after 



PRECESSION OF THE EQUINOXES. 151 

the arrival of the lunar wave — i. e., between the crests of 
the two waves, which are then approaching coincidence. 
On the contrary, after syzygy the high water will be 
before the arrival of the lunar wave. The latter is known 
as the priming, and the former as the lagging of the tide. 
In consequence of this, the intervals between high water, 
though nearly half the lunar day, and on the average 
during the month exactly that amount, will be subject to 
a disturbance, giving rise to longer intervals before and 
shorter intervals after the moon is in syzygy. 

To comprehend in some measure the complicated nature 
of the theory of the tides, which, indeed, has not yet met 
with a complete mathematical solution, the reader must bear 
in mind that the lunar day is not itself of equal length, 
the moon neither moving with uniform velocity nor in 
the equator* Further, the height to which the spring 
tide rises will depend upon the distances of the sun and 
moon from the earth, being greatest, of course, when they 
are in perigee. To a still greater degree it depends upon 
the declination of the sun and moon, since the crest of the 
wave will be vertically below the attracting body. Other 
things being equal, the tide will be highest when the sun 
is on the equator at the equinoxes, the moon not being 
far off.t 

The atmosphere is also affected by similar tidal waves. 
They are very slight, but may nevertheless be observed 
by the barometer. 



II. PRECESSION OF THE EQUINOXES — NUTATION. 

In an early part of this work it was mentioned that 
the equinoxes were not, strictly speaking, fixed points. 

* The same remark applies to the solar day, but to a less 
extent. 

+ We have considered the tides wholly independent of the delay 
and changes the waves undergo in consequence of the tortuous 
course they are often forced to take. This branch of the subject 
plainly belongs to physical geography, though often treated of in 
astronomical books. The establishment of a port, as depending on 
these features mainly, has also not been mentioned. 



152 ASTRONOMY; 

This fact was first discovered by Hipparchus, in conse- 
quence of its effect of constantly increasing the longitude 
of all stars, as any motion of the starting point or zero of 
longitudes must necessarily do. The amount of the 
movement is about 50" -23 per year, and it is caused by 
the attraction of the sun and moon upon the ring of 
matter situated around the earth's equator. We may 
evidently consider the spheroidal figure of the earth under 
this form, and will proceed to trace the effect of the sun's 
attraction upon it at the four positions of the earth, given 
in fig. 22. At the solstice, D, the ring is elevated above 
the sun, but being nearer that body at E than the earth's 
centre is, the pulling force of the sun tends to bring it 
into the plane of the ecliptic — in fact, to make E Q coinci- 
dent with D S, and P p perpendicular to it. If we 
examine the effect on the ring at the farther side of the 
earth, we shall find it precisely the same, and also at the 
other solstice, B. At the equinoxes the sun can have no 
such tendency; but at every other point it will tend more 
or less to bring about this result. In the course of time, 
it would most unquestionably permanently annihilate 
the inclination of the equator to the ecliptic, if the earth 
was not in rotation, which not only opposes this move- 
ment effectually, maintaining the permanence of direction 
of the earth's axis and the constancy of the obliquity of 
the ecliptic to the equator, but forces the perturbation to 
take another form.* 

The effect of the solar attraction is converted from its 
original tendency, and produces instead a slow retrograde 
movement of the point of intersection of the two planes 
along the ecliptic. The manner in which this is produced 
is not easy to explain, but it may be very simply illus- 
trated. If a top is made to spin, and then forced from 
perpendicularity, it does not fall to the ground as it would 

* It is true, the obliquity of the ecliptic is not au absolutely fixed 
angle, and is at present very slowly decreasing ; but this is owing to 
other causes —viz., the mutual action of the planets on one another — 
and further, it is only a secular variation; so that after the lapse 
of many years it will be changed into an increase of the obliquity, 
oscillating between certain definite narrow limits. 



PRECESSION OF THE EQUINOXES. 153 

do if not spinning, but on the contrary, the axis maintains 
its inclination, and slowly revolves around the perpen- 
dicular in the direction of its rotation. This would be 
an exact illustration of precession, if the action of gravity 
had been to draw the axis towards the perpendicular, as is 
the case with the earth, and not from it; the revolution 
of the axis would then have been opposed or retrograde 
to its rotation. 

The time taken for one revolution of the pole of the 
equator round that of the ecliptic, or, what is the same 
thing, for the first point of Aries to perform a complete 
circle round the ecliptic, is 25,800 years. As a conse- 
quence, it follows that the pole star is not the same at 
different epochs. At present the pole of the earth is 
approaching more nearly the direction of the bright star 
Polaris, but it will soon begin to recede from it, and some 
other star coming more nearly in the direction, will then 
be the polar star. Another effect is the constant changing 
of the right ascensions and declinations of all stars, 
planets, &c., since the equinox is the zero, and the motion 
is along the ecliptic (not the equator). The former will 
generally increase; the latter, to a less extent, will either 
increase or decrease, according to their position in the 
heavens; but though the amount is the same each year, 
it will not be uniform throughout that period, being 
nothing when the sun is at the equinoxes. The effect of 
precession on the length of the year has been already 
noted. 

As in the case of the tides, the greater part of the per- 
turbation is to be attributed to the moon's attraction, and 
for the same reason; but the lunar precession is subject to 
an inequality, which causes another change in the position 
of the earth's axis, and which is known as Nutation. 
The moon's attraction tends to bring the earth's equator, 
not into the ecliptic, but into the plane of her own orbit, 
which is inclined to the ecliptic more than 5°. As before 
stated, the nodes of the moon's orbit are in a state of 
rapid retrogression (from a precisely similar cause to that 
which produces the precession of the equinoxes), so that 



154 ASTRONOMY. 

the inclination of her orbit to the plane of the equator 
varies, during the period of the nodal revolution (nineteen 
years), from 2-8- 37', to 18 0, 19 — i.e., by twice the inclina- 
tion to the ecliptic. The lunar contribution to the effect 
of precession will therefore vary, and the movement of 
the poles of the equator round those of the ecliptic will 
be subject to an undulation on either side, of which the 
period is nineteen years. In theory these effects are quite 
distinguishable, that of the nutation being, that the pole 
is carried round in a minute ellipse, with a major axis of 
18 -5", at the same time that it is carried forward in its 
proper circle by the general precession. It also will affect 
the places of all objects, stars or planets. 

III. LUNAR AND PLANETARY PERTURBATIONS. 

When we consider the simple case of one planet revolv- 
ing round a central sun, we find that the movement of 
that body must be a perfect ellipse with the sun in the 
focus, or still more accurately, both bodies will revolve in 
ellipses round the common centre of gravity in an equal 
period and always on opposite sides of that centre. (The 
sun's mass so enormously exceeding that of any planet, 
this point is always situated within the sun, and we may 
thus disregard the motion of that body; such, however, is 
not the case with the earth and moon.) As soon, however, 
as a third body is considered, no perfect ellipse is possible. 
Now, all cases of perturbation reduce themselves to a 
problem of three bodies — a central, a disturbed, and a dis- 
turbing body — which, however, may change places as one 
or other of them forms the subject of enquiry. 

Let us suppose the earth the central, the moon the 
disturbed, and the sun the disturbing body, and trace the 
source of one or two of the lunar perturbations. 1st, 
When the moon is in quadratures, the sun will attract 
the earth and moon equally, but along converging lines ; 
it therefore tends to bring them together, or aids the ter- 
restrial attraction. At the syzygies it tends to separate 
them, because it has the stronger attraction on whichever 



LUNAR AND PLANETARY PERTURBATIONS. 155 

is nearest it. It thus tends alternately to increase and 
diminish the earth's attraction, or it increases the moon's 
velocity before either syzygy, and diminishes it before 
either quadrature. The increased velocity at syzygy 
makes the moon's orbit more straight or flattened there; 
and the reverse taking place at quadrature, it is there 
more curved. The observed effect is, that, during the 
sy nodical revolution, the moon is twice in advance and 
twice behind the place she would have occupied if not 
disturbed by the sun. This is called the moon's variation, 
and was the first perturbation explained by Newton by 
the theory of gravitation. %idly, The sun's power to 
disturb the moon must be greatest in winter, when it is 
nearest to it ; hence arises another inequality depending 
on the eccentricity of the earth's orbit, and known as the 
annual equation. Srdly, Its power must be greater when 
the moon is performing the half of her orbit nearest the 
sun, than when in the other half — hence a parallactic 
inequality. Other perturbations consist in the advance 
of the line of apsides, secular acceleration of its mean 
motion, but greatest of all is a diminishing of the equa- 
tion of the centre at the syzygies, and increasing at 
quadratures, known as the evection. There are, besides, 
others depending on the attraction of Venus. 

The planetary perturbations are all small, owing to 
their great distances from one another. They consist 
chiefly in changes of their eccentricities,^ the positions of 
the nodes and the line of apsides, and the inclination of 
their orbits, The major axes of their ellipses are subject 
to no change, and those of the inclination and eccentricity 
are secular only, varying within certain narrow limits. It 
is upon these facts that the law of the stability of the 
solar system is established. 

Another class of planetary perturbations depends upon 

* The eccentricity of the earth's orbit is at present slowly de- 
creasing — i. e. , it is approaching the form of a circle, which is the 
limit of its change. At one time very remote, it was nearly four 
times more than now; so that the earth must have been much 
nearer the sun at some time of her year than it ever is now, and 
hence must have had a much higher temperature. 



156 ASTRONOMY. 

the near commensurability of some of their periods. Thus, 
five revolutions of Saturn are very nearly equal to eight of 
Jupiter, and thirteen revolutions of Venus to eight of the 
earth. The effect is to bring the planets into conjunction 
(where their attractions on each other are the greatest) 
at nearly, but not precisely, the same points of their orbits. 
This produces an acceleration of the motion of one and a 
retardation of the other, which takes many years to pass 
through its changes. 

As the intention of the present sketch is only to give 
the reader some idea of what this branch of astronomy 
treats, and not to give a summary of perturbations, far 
less their explanations, it is hoped that enough has been 
said to shew that the law which satisfactorily elucidates 
these complicated changes effectually, and indeed fre- 
quently points them out, to be afterwards verified by 
observation, can be none other than the true cause of 
them. Such is the triumphant position, at the present 
day, of the law of gravitation as it was first enunciated 
by Newton. 

QUESTIONS. 

1. Explain the effect of the moon's attraction on the waters of" 
the ocean. Why is a tidal wave formed on the side of the earth 
removed from the moon ? 

2. What is the period of the lunar wave ? What the cause of 
its motion ? and why is it not directly below the moon ? 

3. Does the sun produce tidal waves ? Compare with the 
moon's, and explain why the latter is greater. 

4. What is the period of the solar wave ? What results from 
the difference of the periods? 

5. Explain what is meant by a spring tide; what by neap tide. 

6. Explain the priming and lagging of the tides. When do these 
occur ? 

7. Why are the intervals of high water not equal ? 

S. What two causes tend to produce the highest spring tides ? 

9. Has the atmosphere tidal waves ? How shown ? 

10. By whom and how was the discovery of precession made ? 

11. Explain the effect of the sun's attraction on the spheroidal 
earth at the solstices. Where has it no effect ? 

12. What maintains the constancy of the obliquity of the equator 
to the ecliptic ? 



QUESTIONS. 157 

13. Is the obliquity absolutely permanent ? Of what nature is 
the change it undergoes ? 

14. Give an illustration of precession from the motion of a top. 
In what does the illustration differ ? What lunar perturbation is 
analogous to it ? 

15. What is the period of the revolution of the pole of the 
equator round the pole of the ecliptic ? 

16. What is the effect of the revolution on the pole star ? On 
stars generally ? 

17. Whence arises nutation ? What is its period ? What effect 
has it on the pole of the equator, considered separately and in 
conjunction with precession ? 

18. If the sun had but one attendant planet, describe precisely 
the motion that would arise. 

19. How many bodies have to be considered in discussing any 
perturbation ? 

20. What is the effect of the sun's attraction on the earth and 
moon, when the latter is in quadrature and in syzygy ? 

21. How is the lunar variation produced? 

22. Whence arise the annual equation and the parallactic in- 
equality ? 

23. Of what nature are the planetary perturbations ? Which 
of the elements does not change ? In which is the perturbation 
secular ? 

24. Whence arise the inequalities of long period ? 

25. What change is going on in the eccentricity of the earth's 
orbit ? What effect has that change on terrestrial temperatures ? 



158 



CHAPTER IX. 

SIDEREAL ASTRONOMY. 
I. OF THE FIXED STARS. 

Having now considered all the components of the solar 
system, there remains only the regions of the fixed stars 
to be briefly examined. It is a popular error to suppose 
that these stars are absolutely fixed, although their 
relative positions are subject to such slight changes that 
the lapse of many ages would fail to render them per- 
ceptible to the naked eye. They are, however, doubtless 
in rapid motion, and it is their extreme distance only, that 
produces their apparent fixity. Their numbers are also 
the subject of some exaggeration. Of the brightest class 
or magnitude, there are but 20; of the second, 65; of the 
third, 190; of the fourth, 425; and so on in rapid propor- 
tion ; so that the total number which are brighter than 
the sixth or the faintest magnitude, visible to the naked 
eye, is about 5,000; but even a smaller number — namely, 
-§ , or about 3,300 — is all that rise above the horizon in 
these latitudes, and of course only |-, or 2,500, are all 
that are visible at any particular instant. 

The stars are not equally distributed over the heavens, 
although no particular grouping of the larger stars can 
be noticed. When we examine the distribution of the 
smaller stars, however, from the sixth magnitude down- 
wards to the faintest visible in the largest telescopes, not 
only are they found to be infinite in number, but certain 
districts are found to be enormously rich in stars, while 
others are comparatively barren. The zone of the Galaxy 
or Milky Way is the region of special richness. This band 
of hazy light, so well known to all, has been found to be 
composed wholly of stars too small to appear individually, 
but so crowded as to exhibit the hazy light so character- 



THE MILKY WAY. 159 

istic of this portion of the sky. It extends very nearly 
in a great circle of the heavens, of variable breadth, and 
sometimes with brief gaps (one of these, in the southern 
heavens, forms the well-known coal sack), but is generally 
continuous. During one part of its course it is split into 
two parallel streams, which eventually unite again. The 
most probable explanation of the peculiar grouping is, 
that the solar system is situated towards the centre of a 
mass of bodies similar to our own sun, which collectivel} 
have the form of an immense and somewhat irregular 
lens. This supposition accounts for the great number of 
stars of the smaller magnitudes, which lie in the direction 
of the Milky Way, or that of the breadth of the lens, and 
which extends to a much greater distance than what we 
must consider the thickness of the lens, or those much 
more extensive regions of the sky where the stars are 
comparatively few. But it must be remembered that 
the individual members of this group are probably as 
isolated from one another as we are from them. 

It is only within the last fifty years that any satisfactory 
results have been arrived at regarding the distances of any 
stars whatever, and still our information on this point is 
very meagre. In order that this difficult problem may 
be solved, it is necessary to observe the precise position of 
a star as seen when the earth is situated at opposite points 
of her orbit. Such measurements being taken, they must 
be cleared of the effect of precession during the interval, 
as well as of the total effect of nutation and aberration; and 
when these corrections have been made, it is found that 
the star occupies almost precisely the same position at 
the two epochs. In this way it has been repeatedly 
proved that the diameter of the earth's orbit, great as it 
is, must be absolutely insignificant compared with the 
distance of the star under discussion. The refined 
instruments of modern times have, however, at length 
shown that some very small parallactic displacement may 
be observed and measured for a few stars. In no case 
does the observed displacement exceed 2", or indicate 
an annual parallax of 1". One star (# Centauri) very 



160 ASTRONOMY. 

nearly approaches this limit, and is believed to be the 
nearest fixed star. Its annual parallax has been found, 
with considerable certainty, to be 0"-91o8, which is 
equivalent to a distance of 20,590,500,000,000 miles, or 
roughly, twenty billions of miles. Such is the enormous 
distance of the nearest fixed star! It would require more 
than 3 J years for light to travel from « Centauri to the 
earth, though its velocity is equal to 184,000 miles in a 
second. 

There are about ten other stars whose parallax has 
been found to be sufficiently large to be measurable ; and 
of this group the most interesting is perhaps 61 Cygni. 
The parallax of this star — and it was the first that yielded 
a satisfactory result — was determined by Bessel to be 
0"*3483, which is equivalent to a distance of 2f times that 
of ct Centauri, and to travel which, light would requii/e 
9^ years. This star has been found to have a most 
rapid motion of its own (the fact which pointed it out as 
likely to be one of the nearest of the stars) ; and since we 
have now found its distance, we are able to discover its 
absolute velocity. It has been found that the star is 
moving at the rate of 1,280 millions of miles per annum— 
a fact that at once dispels the idea of fixity, a Centauri 
has an absolute movement about one-fourth as great. 

It is evident that we have at present very insufficient 
data on which to found general ideas of the average dis- 
tances of the stars. jSTone have yet been found whose 
distance is not greater than those of the two above 
mentioned ; but it would appear that although the 
fainter stars may generally be more distant than the 
brighter, yet the distance of a particular star cannot be 
even approximately inferred from its faintness. Thus, 
the star 61 Cygni is of the sixth magnitude; and some of 
the first, whose parallax has been determined, are two or 
three times more distant than it; and- in the case of others 
no sensible annual parallax whatever has been found. Still, 
it must be accepted that the very faint stars visible in 
large telescopes must be immensely beyond those visible 
to the naked eye; and supposing such to be suns equal in 



OF THE FIXED STARS. 161 

size and brightness to onr own, we are obliged to conceive 
them at distances so remote, that light would take upwards 
of 3,000 years to reach us from thence. There is thus 
neither limit of distance nor of number to the fixed stars. 
Each successive increase of optical power brings into 
view fainter and fainter specks of light, to which we are 
obliged to attribute greater and greater distance. These 
remarks apply principally to the Milky Way, as it is 
possible, that in other regions the largest telescopes may 
pierce through the stratum of stars to regions beyond. 

The distances of the stars having in a few instances now 
been found, it becomes an important question to discover, 
whether there are any means at our command by which we 
may arrive at some approximate estimation of the dimen- 
sions of any of these bodies. The discs of stars which are 
seen in good telescopes being known to be spurious — i.e., 
produced by optical phenomena, and no true indication of 
the diameter of the star — we are obliged to judge solely by 
a comparison of their light with that of the sun. Not- 
withstanding the difficulty of such an unequal comparison, 
it has been effected ; and the general result is, that if the 
sun was removed to the distance of the fixed stars, it would 
shine as a star of average magnitude. In the case of 
u Lyrse, the brightest star in the northern heavens, and 
whose parallax is 0"-261, it has been found that its intrinsic 
brilliancy is three and a-half times that of the sun ; or, 
supposing their surfaces equally bright, the diameter of the 
star will be nearly twice that of the sun. From a similar 
comparison with Sirius, the most brilliant of all the stars, 
and whose parallax is only 0"-150. it has been found that 
the sun has probably but yi^ part of the lustre of this star, 
and that supposing its surface no more brilliant than the 
sun's, it must have a diameter more than twelve times 
as great as it. On the other hand, 61 Cygni, and the next 
four nearest stars at present known as such, must be many 
times less in splendour and size to our own sun. 

When the positions of stars, as observed at remote 
epochs, are compared, due allowance having been made for 
precession, &c., it is found that many, and perhaps all 

A. L 



162 ASTRONOMY. 

have more or less motion, so slight as only to be per- 
ceptible after long intervals, yet certainly established, and 
generally uniform in direction and amount for each star. 
61 Cygni has a motion exceeding 5" per year; but this is 
exceptio rally great, the vast majority of even bright stars 
having much less proper motion than this. If, however, 
this motion was found to be general and similar in direc- 
tion for all stars — if there was a tendency manifested for 
all stars to move away from one particular spot in the 
heavens, and to crowd together towards a spot diametri- 
cally opposite to this — the cause would clearly have to be 
traced to the movement of the sun, with its attendant 
planets in space, towards that point from which the stars 
appeared to move, rather than to the fact that all the 
stars had a common motion. This has been found to be 
the case; and though there are still outstanding indepen- 
dent motions, belonging doubtless to the stars themselves, 
and various in direction, still a large part of the movement 
of all the stars used in the determinations (a very con- 
siderable number) is accounted for by supposing the sun 
to be in motion towards a particular spot in the heavens, 
near to a star called n Herculis. The amount of this 
proper motion of our own sun in a year, has been found 
to be equal to 1§ times the earth's radius vector, or about 
150 millions of miles. It is impossible at present to 
determine more than the direction and velocity of the sun's 
motion, and ages must elapse before it can be found 
whether its path deviates from a straight line, and if 
curved, round jwhat point and in what precise figure. 



OF DOUBLE AND VARIABLE STARS. 

When the fixed stars are examined individually, either 
by the unaided eye or by the telescope, they are found to 
differ from each other in more respects than simply in 
brightness. Telescopes of very small power are frequently 
able to resolve a single star into two or more stars situ- 
ated very close to each other. These are known as Double 



OF DOUBLE AND VARIABLE STARS. 163 

or Multiple stars. In very many cases the two component 
stars are unequally bright, and may be at immense dis- 
tances from one another, being simply situated very 
nearly in the same direction, as regards the spectator. 
Such are said to be only optically double, their apparent 
nearness being the effect of perspective, and they are only 
interesting in so far that the more distant, and hence 
more fixed star, may help to bring to light either the 
proper motion or the parallax of its brighter and nearer 
companion, by means of the measurement of their angular 
distances at different epochs. 

It is, however, very frequent to find the stars nearly 
equal in brightness, and so conspicuous that their near- 
ness, on the law of chances alone, can only be accounted 
for by supposing a physical connection. This is occa- 
sionally still further confirmed by finding that the two 
components have a precisely similar proper motion. It is 
not, however, usually assumed that they are actually con- 
nected, until some revolution of the one round the other 
has been observed. They are then classed as binary stars, 
or systems connected by the law of gravitation, and their 
relative motions, as they revolve slowly around each other, 
are watched with great interest. Sir William Herschel 
was the first who made extensive searches for double stars, 
and measurements of their relative positions and angular 
distances, with the view of detecting, after a time, 
any motion of the one star round the other. At the 
present day as many as 650 have been clearly established 
to be true binary systems, and many others will probably, 
in the course of some years, be added to the number. 
The components of these are by no means invariably 
equal in brightness; so that large numbers at present 
classed as optically double only, may be found to be physi- 
cally connected, though many of that purely casual class 
must exist. The total number of double stars known is 
about 6,000. 

From the relative positions and distances of binary 
stars at different epochs, it has been found possible to 
determine the elements of the stellar orbits, and to estab- 



1 64 ASTRONOMY. 

lish the strict applicability of the law of gravitation to 
these distant suns. A very few have made complete 
revolutions since they have become objects of exact mea- 
surement, and many have performed a considerable part 
of a revolution. Their orbits are ellipses (sometimes 
viewed so as to be much foreshortened) round their 
common centre of gravity, and performed in various 
periods — from 30 to 1,000 years. Both the stars * 
Centauri and 61 Cygni are well-known binary systems, 
and their parallax being known also, we are able to find 
the absolute dimensions of their orbits with pretty close 
approximation. The components of the former star are 
about as distant from each other as Uranus from the sun, 
and those of the latter about half as far again as Neptune, 
exceeding the aphelion distance of Halley's comet. 

Another peculiarity of individual stars, and which is 
found to exist very conspicuously in the case of double 
stars, is variety of colour. The great majority of all stars 
are white or pale-yellow, like our own sun, but many also 
have most pronounced and deeply-marked colours. The 
most interesting and numerous class of isolated coloured 
stars are those which shine with a red light, of which 
about 300 examples are known, varying from the deepest 
crimson to orange. The orange and yellow stars also 
form a numerous class; but very few indeed, of any other 
colour are to be found among isolated or unaccompanied 
stars. In double stars, however, it is frequent to find the 
two members of different and strongly contrasted colours, 
as red and green, yellow and blue, orange and purple. 
This, in some cases, may be purely the effect of contrast, 
the fainter star being really white, but it is also shown to 
be actually the case in many instances. If such systems 
are surrounded by revolving planets, the inhabitants (if 
any) will have days of variously-coloured light. It is 
frequent also to find the components of a double star 
similar in colour, but the fainter of a deeper tint. 

There is some reason to believe that the colour of a 
star may vary; and in one instance — that of the bright 



OF DOUBLE AND VARIABLE STARS. 165 

star Sirius — it is historically ascertained that a change of 
colour has taken place. To the ancients this star was un- 
doubtedly red, and was classed by them with a Ononis, 
Aldebaran, and others that have still that colour; but' 
Sirius is now a brilliant white star. A temporary star 
that was seen in 1572 by Tycho Brahe still more cer- 
tainly changed its colour. This star was only visible for 
seventeen months, appearing suddenly of a most brilliant 
white lustre. It was afterwards seen to change to yellow 
and red, and then again, as it was growing fainter, to 
white again. 

The apparition of temporary stars is so rare a phe- 
nomena that very little is known about them. The star 
above mentioned is the most remarkable, and of recorded 
instances is perhaps the brightest, having been visible in 
the daytime. They have always been considered as peri- 
odical; but perhaps this is doubtful. About twenty 
instances are on record of the sudden appearance of a new 
star, but in no case has it long retained the brightness 
with which for a period it shone ; so that a temporary 
catastrophe, rather than a natural increase of lustre, 
would appear to be the cause of the change. This' is 
strongly confirmed by the latest apparition of a new star, 
which occurred in 1866, in Corona, when a very small 
but known and permanent fixed star suddenly attained 
the'second magnitude, and slowly faded, with slight alterna- 
tions during several months, till it reached its original 
degree of faintness. The spectroscope revealed the 
astonishing fact that this additional brightness was caused 
by the ignition of the gas, hydrogen. It must be remem- 
bered that, owing to the gradual propagation of light, this 
catastrophe must have happened many years, possibly 
many ages, before it was seen by us. Whether all tem- 
porary stars are produced by like catastrophes, or whether 
they are simply variable in brightness, taking a long 
interval for their periodical changes, must for the present 
remain unsettled. Connected with this subject is the 
fact, that some stars known and catalogued by the 



166 ASTRONOMY. 

astronomers of ancient times have now entirely dis- 
appeared. 

The next class of stars that we have to consider 
resembles in some degree the temporary stars — that is, 
they are found to be variable in their magnitude or bright 
ness. They form a tolerably large class, of which each 
member has its own distinctive features. One of the best 
known, and whose variability is most easily recognizable, 
is o Ceti. It varies from the second to the twelfth magni- 
tude in a period little less than a year (331*34 days). It 
maintains its maximum brightness about fifteen days 
only, and is invisible to the naked eye during five 
months. Another well known variable (Algol or /3 Persei) 
strongly suggests the presence of some dark body revolv- 
ing round it, and periodically occulting it partially. It 
is usually of the second magnitude, but suffers a diminu- 
tion to the fourth magnitude for the space of a quarter 
of an hour, at intervals of only 2*867 days. The southern 
star, yi Argus, is still more remarkable, its changes being so 
capricious that it has not been found possible as yet to 
establish a regular cycle of them. It is sometimes as 
faint as the sixth magnitude, and at others ranks among 
the brightest of first magnitude stars, being surpassed by 
Sirius alone. The above are given as examples of the 
nature of stellar variability; but a few stars are known 
that totally disappear for a time, and regularly attain to 
very considerable brightness, while in others the variation 
is but slight, requiring careful comparison to be detected 
at all. The periods are vaiious, but many, and these the 
most remarkable, do not exceed a year — in some, as Algol, 
it is only a few days. 

The rapid changes of intensity of light, as well as of 
colour of stars, known as scintillation or twinkling, are 
unconnected with the stars themselves. They form one 
of the numerous phenomena of interference depending on 
the undulatory motion of light, when passing through 
strata of various densities. For this reason twinkling takes 
place mostly near the horizon, where the ray has to pass 



CLUSTERS OF STARS. 167 

through a very thick stratum of air. In tropical regions, 
where the atmosphere is more homogeneous, twinkling is 
never noticeable except very near the horizon. The 
planets do not twinkle, owing to their comparatively 
large discs, and the light of some stars appears to scintil- 
late more than that of others. 



III. CLUSTERS OF STARS NEBULA. 

Small local aggregations of stars exist in many parts of 
the heavens, besides the great concentration in the ring 
of the galaxy. A few of these are sufficiently bright to 
be seen by the naked eye. The Pleiades will occur to 
every one as a rich spot, and others, as Prassepe in Cancer, 
the sword-hilt of Perseus, &c, may be found as hazy 
spots of light when viewed by the unaided eye, which a 
very slight optical power shows as clusters of stars. 
Several thousands of these groups lie scattered over the 
heavens; and in some the stars are so densely packed, 
and are so very minute, that a powerful telescope is 
required to show them as composed of separate individual 
stars; and there are still some which defy the highest 
optical means that can be brought to bear upon them, and 
which remain as faint milky patches, resembling cloud, 
under the highest magnifying powers. The term nebulae 
is applied to these irresolvable groups, though many of 
them, and at one time all, were thought to have a struc- 
ture entirely distinct from vaporous cloud. 

True nebulae, it is now known, really exist, and that 
there are, at the most extreme distances from us, immense 
tracts of nebulous matter capable of radiating light, and 
subject possibly to the dynamical laws peculiar to them- 
selves. Some of these patches extend over an apparent 
area several times greater than the moon, and their real 
dimensions must be enormous beyond anything of which 
we can form conception. Their forms, too, are as various 
as their character is anomalous; and there are not wanting 



16$ ASTRONOMY. 

suspicions of strange alterations of form and brilliancy, 
which have invested these distant objects with a great 
deal of interest. They have been divided into several 
classes, according to their form, but perhaps not altogether 
successfully. Thus the elliptical nebulae constitute one 
well-marked class — this form being frequent. One of 
these, in Andromeda, is bright enough to be visible to the 
naked eye, and has often been mistaken for a comet. 
Sometimes nebulae present a flat planetary disc, at others 
strangely convoluted spiral forms. Some are found 
circularly surrounding a star, which is frequently a red 
one ; but many most important, large, and bright nebulae 
are so irregularily shaped as to defy classification. 

When the distribution of these nebulous spots over the 
heavens is examined, they are found to be extremely 
numerous near the poles of the Milky Way — that zone 
itself being nearly destitute of them. Easily resolvable 
clusters are found, on the contrary, to be more numerous 
in the vicinity of the galaxy. In the southern hemi- 
sphere both clusters and nebulae are extremely numerous 
in two spots, which thus present a remarkable appearance 
to the naked eye, and are known as the Magellanic 
clouds. 

It may be conjectured that clusters are distant con- 
geries of stars, similar to the bright galaxy of which our 
own sun forms probably an individual member ; but it is 
necessary in this case to assume their distances as being 
most enormous, so that light ' would require many 
thousands of years to reach us from thence. The faint- 
ness of the component stars in most cases favours this 
supposition, however. For any insight into the physical 
constitution of the nebulae proper, we must wait till the 
continually increasing powers of our telescopes enable us 
with more ease and certainty to delineate their forms and 
trace their changes. They are probably, at least, as 
distant as the clusters ; but their nature is such that we 
cannot hope for an early solution of the difficulties in- 
volved. 



QUESTIONS. 169 



QUESTIONS. 

1. Give some idea of the numbers of the brighter stars, and of 
those visible to the naked eye. 

2. What is known of the distribution of the fainter stars, and 
whence arises the nebulous light of the Milky Way? 

3. How is the grouping of the smaller stars explained? 

4. How are the parallaxes of the stars measured, and with what 
general results? 

5. State the parallax and distance of the nearest fixed star, and 
the time of its light reaching the earth. 

6. Give the same particulars for 61 Cygni, the second nearest 
star. For what is 61 Cygni remarkable? 

7. To what extent is the faintness of stars a guide to their 
distances ? 

8. How do we arrive at an estimate of the true dimensions of 
stars? State some results of such estimation. 

9. How is the proper motion of a star found ? 

10. Supposing the sun to be in motion, what effect would be 
noticeable in the fixed stars? Is this effect really observed? 

11. Does the supposition of the sun's movement in space account 
for all the observed proper motions? Towards what star is the 
sun moving, and with what rapidity? 

12. What is meant by double and multiple stars ? Distinguish 
between optically double and binary stars. 

13. What may the observation of optically double stars bring to 
light? State the reasons for believing binary stars to be actually 
connected. 

14. State the number of known double stars, and of these, how 
many are recognized binary systems? 

15. In what orbits do the binaries revolve, and in w T hat periods? 
Give the dimensions of the orbits of 61 Cygni and a Centauri. 

16. What colours predominate among isolated stars? State 
the number of known red stars. 

17. What peculiarities are frequently observed in the colours of 
double stars? 

18. What is the colour of the star, Sirius? Has it changed? 

19. State peculiarities of colour and brightness of Tycho Brahe's 
temporary star. 

20. How many instances of temporary stars are on record? 
Give the history of the star of 1866. Have stars disappeared 
permanently ? 

21. Give examples of variable stars, the amount and period of 
their variability. 

22. What is the suspected cause of the variability of .Algol? 
Within what limits are the periods of variables mostly confined ? 
What southern star is a notable exception ? 



1 ?0 ASTRONOMY, 

23. To what cause is the scintillation of stars traceable? Why 
is the phenomena little noticed in the tropics? 

24. What are clusters? Distinguish them from nebulae. Do 
true nebulae exist ? 

25. Give some classes into which nebulae have been divided. 

26. Where are nebulae mostly found? Where clusters? 

27. What are the Magellanic clouds ? What is the coal sack ? 
Explain the probable constitution of clusters. 



INDEX. 



Aberration, 62. 

Aberration, diurnal, 63. 

Aberration time. 63. 

Achromatism, 39. 

Adams, 133. 

Airy, 13. 

Albedo, 103. 

Algol, 166. 

Altair, 28. 

Altazimuth, 39. 

Altitude, 27. 

Angle of the vertical, 55. 

Annular eclipse, 106. 

Anomaly, 49. 

Aphelion, 48. 

Apogee, 97. 

Apsides, line of, 49. 

Aiago, 140. 

Aristarohus, 58. 

Asteroids, number known, 118. 

„ size of, 119. 

„ their brilliancy, 119. 

„ orbits, 119. 

„ periodic times, 120. 
Atmosphere, constitution of, 19. 
Augmentation of moon's semi- 
diameter, 98. 
Axis of the earth permanent in 

direction. 88. 
Azimuth, 27. 

„ error of, 34. 

Base line, measurement of, 11. 
Bessel, 13, 160. 
Binary stars, 163. 

„ number recognized, 

163. 

„ orbits of, 164. 

„ distances and 

periods of, 164. 
Biela's comet, 144. 
Bode's law, 68. 
Bradley, 61, 125. 

Calendar, arrangement of, 43. 
Camilla, 120. 
Cancer, tropic of, 29. 
Capricorn, tropic of, 29. 
Cavendish experiment, 96. 
Ceres, 119. 

Chromatic dispersion, 39. 
Chromosphere, 78. 



Clusters of Stars, 167. 
Collimation, line of, 34. 

„ error of, 34. 

Coma, 137. 
Comets, probable numbers, 137. 

„ changes of form, 138. 

„ mass of, 139. 

„ their tenuity, 139. 

„ brilliancy, 140. 

„ orbits, 140. 

„ inclination of orbits, 141. 

„ heat sustained by, 142. 

„ perihelia of, 141 

„ aphelia of, 142. 

„ tails of, 142. 
of H alley, 143. 

„ of Encke, 144. 
of Biela, 144. 

„ of Donati, 145. 

„ orbits identical with 

those of meteors, 145. 

„ Tempel's, 146. 
Conic sections. 53. 
Conjunctions of inferior planets, 

66. 
Conservation of areas, law of, 49. 
Copernicus, 47, 115. 
Corona, 78. 

Craters of the moon, 104. 
Cyclones, rotation of, 18. 

Day, sidereal, solar, and lunar. 

41. 
Decimation, 28. 
Diffraction, £3. 
Dip of the horizon, 10. 
Direct motion, 46. 
Dollond, 39. 
Double stars, 162. 

,, their numbers. 163. 

„ colours, 164. 

„ orbits, 163. 



Earth, curvature of, 10. 
its diameter, 13. 
form, 9. 

circumference, 12. 
ellipticity, 13, 16. 
eccentricity of orbit, 83. 
bulk, 93. 
density, 94, 97. 



172 



INDEX. 



Earth, mean distance from sun, 88. 
„ its distance how found, 59. 
„ rotation of, 14. 
Earthshine, 103. 
Eccentricity, angle of, 49. 

„ of planetary orbits 

liable to chauge, 155. 
Eclipse of the moon 105. 

„ sun 106. 

Eclipses of Jupiter's satellites, 123. 
Ecliptic, 30. 

Elongations of inferior planets, 66. 
Encke, 144. 
Epact, 99. 
Equation of the centre, 49. 

„ time, 42. 

Equatoreal, 38. 

Equatorial horizontal parallax, 58. 
Equinoctial, 28. 

„ colure, 32. 

Equinox, 29. 
Evection, 155. 

Faculje, 76. 

First point of Aries, 28. 
„ Libra, 31. 

Flora, 120. 
Focus, 33. 
Foucault's pendulum experiment, 

14. 
Frequency of eclipses, 110. 

Galaxy, 158. 
Galileo, 72, 122, 124. 
Glass specula, 40. 
Gravitation, law of, 54. 
Great Bear, 32. 
Gregorian Calendar, 44. 
Gregory, 39. 
Gyroscope, 15. 

Halley, 60. 
Harvest moon, 98. 
Heliocentric co-ordinates, 133. 
Herschel, 73, 130. 
Hipparchus, 47, 152. 
Horizon, rational, 108. 
Hour angle, 31. 
Hyperbolic orbits, 141. 

Inferior Planets, 66. 
Irradiation of Light, 82. 

Japetus, 129. 

Julian Calendar, 43. 

Jupiter, apparent diameter, 120. 

„ brilliancy, 120. 

„ bulk, mass, and density 
of, 122. 

„ belts of, 121. 

„ distance from sun, 120. 

„ ellipticity of form, 120. 

„ eccentricity of orbit, 120. 

„ real diameter, 121. 

„ rotation of, 122. 



Jupiter, satellites, 122. 

„ sidereal and synodical 

periods, 120. 
„ spots upon, 121. 

Kepler, 47, 82, 115. 
Kepler's laws, 47. 

Lapissa, eclipse of, 111. 
Latitude, 30. 

„ geographical, to And, 91. 
„ length of degree of, 12. 
Level, error of, 34. 
Le Verrier, 133. 
Libration, diurnal, 101. 
„ in latitude, 100. 
„ in longitude, 101. 
Light, aberration of, 62. 

„ velocity of, 125. 
Limits of visibility of eclipses, 107. 
Longitude, 30. 

„ terrestrial, to find at 

sea, 92. 
Lunar ecliptic limits, 109. 
,, perturbations, 154. 
Lunation, 99. 

Magellanic clouds, 168. 
Mars, apparent diameter, 115. 
„ brilliancy. 115. 
„ climate of, 117. 
,, distance from sun, 115. 
„ phases of, 116. 
„ polar compression of, 118. 
,, eccentricity of orbit, 115. 
„ real diameter, 115. 
„ intensity of light on. 117. 
„ sidereal and synodical re- 
volutions, 115. 
„ mass and density, 116. 
„ rotation of, 117. 
„ surface of, 118. 
Mean solar day, 41. 
Mean sun, 42. 

Mercury, apparent diameter, 68. 
„ distance, 81. 
„ eccentricity of orbit, SI. 
„ mass and density of, 82- 
,, transits of, 82. 
„ mountains on, 82. 
„ real diameter, 81. 
„ rotation of, 81. 
,, sidereal and synodical 
periods, 80. 
Meridian, 31. 
Meridional arc, 12. 
Meteors, 145. 
Metonic cycle, 100. 
Milky way, 158. 
Moon, mean distance of, 97. 
„ apparent diameter, 97. 
„ real diameter, 98. 
„ bulk of, 98. 
„ mass and density, 101. 
„ gravity on surface, 102. 



INDEX. 



173 



Moon, sidereal and synodical re- 
volutions, 99. 

„ rotation of, 100. 

,, eccentricity of orbit, 97. 

„ probable form, 98. 

„ inclination of orbit, 98. 

„ phases, 102* 

„ mountains on, 104. 

„ parallax, how found, 57. 
Motion, laws of, 51. 
Mountains, attraction of, 93. 
Mural circle, 35. 

Nadir, 27. 
Nebulae, 167. 

„ classification of, 168. 
„ distribution of, 168. 
Neptune, discovery of, 133. 
„ period, 134. 
,, distance, 134. 
„ diameter, 134. 
„ mass and density, 134. 
„ intensity of light upon, 

134. 
„ eccentricity of orbit, 134. 
Newton, 51, 95, 140, 149. 
Nodes, line of, 50. 
„ lunar, retrogression of, 
110. 
Noon, mean and apparent, 42. 
Nucleus of comets, 137. 

,, of solar spots, 73. 
Nutation, 153. 

Object glass, 33. 
Oblate spheroid, 13. 
Obliquity of the ecliptic, 32. 

its variation secular, 152. 
Occupations, 103. 

„ of Jupiter's satel- 

lites, 124. 
Octants, 103. 
Olbers, 118. 
Opposition, Q6. 

Parabolic orbits of comets, 141. 
Paraboloid of revolution, 39. 
Parallactic inequality, 155. 
Parallax, 56. 

„ of the moon, 57 

„ of the sun, 58. 

„ of Mars, 61. 

,, annual, 61. 

,, of stars, 159. 

,, correction for geocen- 
tric, 37. 
Pendulum, length of, 16. 

„ Foucault's, 14. 

„ density of the earth 

measured by, 95. 
Penumbra, in eclipses, 106. 

„ of solar spots, 73. 

Perigee, 97, 125. 
Perihelion, 48. 
Periodic times, law of, 49. 



Perturbations, 55, 149, 154. 
Phases of inferior planets, 67. 

,, of the moon, 102. 
Photosphere, 74. 
Planets, superior and inferior, GG. 

„ retrogradations of, 46, 83, 
116. 

., phases of, 67, 116. 
Pleiades, 167. 

Plumb line, direction of, 12, 55. 
Polar distance, 31. 
Polariscope, 140. 

Poles, celestial revolution of, 
153. 
„ of ecliptic, 32. 
Pope Gregory XIII.. 43. 
Preesepe, in Cancer, 167. 
Precession of the equinoxes, 151. 
Priming and lagging of the tides, 

151. 
Principia, 141. 
Prolemaic system, 47. 
Proper motion of stars, 162. 

„ of the sun, 162. 

Pythagoras, 47. 

Quadrature, 102. 

Radiant point of meteors, 146. 
Radius vector, 48. 
Redness of moon in eclipse. 112. 
Reformation of calendar, 43. 
Reflecting telescopes, 39. 
Refraction, 20. 

„ law of atmospheric, 

21. 
Resisting medium, 144. 
Retrograde motion, 46. 
Right ascension, 28. 
Rings of Saturn, 127. 

„ their dimensions, 123. 
,. phases of, 129. 

inclination, 129. 
„ physical constitution of, 130. 
„ mass, 130. 
Roemer, 32, 62, 124. 
Rotation, diurnal, 13. 

„ „ proof of, 14. 

„ of planets, 68. 

„ of Saturn's rings, 128. 

Saros, 110. 

Satellites of Jupiter, 122. 

„ their distances, 123. 

„ periodic times, 123. 

„ eclipses of, 123. 

„ rotation, 123. 

„ their dimensions, den- 
sity, and mass, 126. 

„ of Saturn, 127. 

„ their inclination, 129. 

„ of Uranus, 131. 

„ of Neptune, 134. 
Saturn, distance of, 127. 

„ eccentricity of orbit, 127 



174 



INDEX. 



Saturn, sidereal and sy nodical 
periods, 127. 

,, diameter, 128. 

„ ellipticity, 128. 

„ rotation, 12S. 

„ • mass and density, 130. 

„ rings of, 127. 

,, satellites, 127, 129. 
Schehallien experiment, 93. 
Schwabe, 74, 77. 
Scintillation, 166. 
Seasons, 89. 
Sidereal day, 41. 

„ time, 35. 

„ year, 43. 
Sirius, 28, 161, 165. 
Solar day, 41. 

„ eclipse, theory of, 106. 

„ „ phenomena witnessed 
during, 77. 

„ ecliptic limits, 109. 

,, system, 66. 

„ ,, general view of, 69. 
Solstice, 29. 
Solstitial Colure, 32. 
Spectroscope, 140, 165. 
Speculum, 40. 
Spheres, attraction of, 55. 
Spots on the sun, description of, 72. 

, . degree of light from, 73. 

,, magnitude of, 73. 

„ duration, 74. 

„ explanation of, 74. 

,, regions where found, 76. 

,, periodicity, 77. 
Stars, diurnal movements of, 13. 

„ numbers and magnitude of, 
158. 

„ distribution, 158. 

„ parallax of, 159. 

„ proper motion of, 160. 

„ estimated size of, 161. 

„ double, 162. 

„ coloured, 164. 

„ variability of colour in, 164. 

„ temporary, 165. 

„ missing, 165. 

„ variable, 166. 
Style, old and new, 44. 
Sun, distortion of figure on 
horizon, 22. 

„ parallax of, 60. 

„ apparent and real diameter 
70. 

„ distance from' earth, 70. 

„ bulk, 70. 

„ mass and density, 71. 

„ gravity on surface, 72, 

„ rotation of, 72, 75. 

„ atmospheres, 78. 

„ heat received from, 79. 

„ motion in space, 162. 



Superior planets, 6G. 
Survey, trigonometrical, 11. 
Synodical revolution, 67. 
Syzygy, 103. 

Telescope, 33. 
Terminator, 104. 
Thales, eclipse of, 111. 
Tides, cause of, 149. 

„ spring and neap, 150. 

„ priming and lagging of, 151. 

„ atmospheric, 151. 
Time, measurement of, 40. 
Titan, 130. 

Trade winds, cause of, 17. 
Transit instrument, 32. 

„ circle, 37. 
Transits of inferior planets, 59, 82. 
Tropics, 29. 
Tropical year, 43. 
Twilight, explanation of, 22. - 

„ duration, 24. 
Tycno Brahe, 35, 47, 165. 

Ultra-zodiacal planets, 119. 

Umbra, 106. 

Uranus, discovery of, 130. 

„ distance, 131. 

„ period, 131. 

„ real and apparent dia- 
meter, 131. 

„ satellites of, 131. 

„ mass and density, 131. 

„ eccentricity of orbit, 131. 

„ intensity of light on, 132. 

Variation, lunar, 155. 
Velocity of light, 125. 

„ of motion in orbits, 141. 
Venus, transits of. 59, So. 

„ distance, 83. 

,, . eccentricity of orbit, S3. 

„ sidereal and synodical 
periods of, 83. 

„ apparent diameter, 68. 

„ true diameter, 83. 

„ mass and density of, 84. 

„ brilliancy, 84. 

„ rotation, 84. 

„ atmosphere, 84. 

,, mountains on, 85. 
Vesta, 119. 

Weight of bodies in different 
latitudes, 15. 

Zenith, 27. 

„ distance, 81. 
sector, 12, 93. 
Zodiac, 50. 
Zodiacal light, 79. 



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